main.bib

//
// this is the bibtex file used to compile the bibliography for the sigma orientation course notes.
// whenever possible, citations should be pulled from mathscinet, pasted in exactly, and then their identifiers should be changed to something human-readable, subject to the following guidelines:
//
// 1) if there are one or two authors, list their last names in alphabetical order (e.g., AndoStrickland).
// 2) if there are three or more authors, list their last initials in alphabetical order (e.g., BCM).
// 3) if these rules result in name collisions (e.g., the Ando Hopkins Strickland papers), a short string related to the title of the paper should be appended with word-initial capitals (e.g., AHSHinfty and AHSTheoremOfTheCube).
//

@book {AdamsBlueBook,
    AUTHOR = {Adams, J. F.},
     TITLE = {Stable homotopy and generalised homology},
    SERIES = {Chicago Lectures in Mathematics},
      NOTE = {Reprint of the 1974 original},
 PUBLISHER = {University of Chicago Press, Chicago, IL},
      YEAR = {1995},
     PAGES = {x+373},
      ISBN = {0-226-00524-0},
   MRCLASS = {55-02 (57-02)},
  MRNUMBER = {1324104 (96a:55002)},
}

@article {AdamsClassifyingSpacesII,
    AUTHOR = {Adams, J. F.},
     TITLE = {Maps between classifying spaces. {II}},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {49},
      YEAR = {1978},
    NUMBER = {1},
     PAGES = {1--65},
      ISSN = {0020-9910},
   MRCLASS = {55R40 (55R35 55R50)},
  MRNUMBER = {511095},
MRREVIEWER = {C. B. Thomas},
       URL = {https://doi.org/10.1007/BF01399510},
}

@article {AdamsJXIV,
    AUTHOR = {Adams, J. F.},
     TITLE = {On the groups {$J(X)$}. {IV}},
   JOURNAL = {Topology},
  FJOURNAL = {Topology. An International Journal of Mathematics},
    VOLUME = {5},
      YEAR = {1966},
     PAGES = {21--71},
      ISSN = {0040-9383},
   MRCLASS = {55.40},
  MRNUMBER = {0198470},
MRREVIEWER = {E. Dyer},
}

@book {AdamsInfiniteLoopSpaces,
    AUTHOR = {Adams, John Frank},
     TITLE = {Infinite loop spaces},
    SERIES = {Annals of Mathematics Studies},
    VOLUME = {90},
 PUBLISHER = {Princeton University Press, Princeton, N.J.; University of
              Tokyo Press, Tokyo},
      YEAR = {1978},
     PAGES = {x+214},
      ISBN = {0-691-08207-3; 0-691-08206-5},
   MRCLASS = {55-02 (55N20 55P47)},
  MRNUMBER = {505692},
MRREVIEWER = {Stewart B. Priddy},
}

@incollection {AdamsOnCobar,
    AUTHOR = {Adams, J. F.},
     TITLE = {On the cobar construction},
 BOOKTITLE = {Colloque de topologie alg\'{e}brique, {L}ouvain, 1956},
     PAGES = {81--87},
 PUBLISHER = {Georges Thone, Li\`ege; Masson \& Cie, Paris},
      YEAR = {1957},
   MRCLASS = {55.0X},
  MRNUMBER = {0090045},
MRREVIEWER = {S. Eilenberg},
}

@article{AdamsPrimitiveElts,
  title={Primitive elements in the {$K$}-theory of {$BSU$}},
  author={Adams, J Frank},
  journal={The Quarterly Journal of Mathematics},
  volume={27},
  number={2},
  pages={253--262},
  year={1976},
  publisher={Oxford University Press}
}

@article{AdamsVFoS,
  title={Vector fields on spheres},
  author={Adams, J Frank},
  journal={Topology},
  volume={1},
  number={1},
  pages={63--65},
  year={1962},
  publisher={Elsevier}
}

@article{AdamsAtiyah,
  title={K-theory and the Hopf invariant},
  author={Adams, John Frank and Atiyah, Michael F},
  journal={The Quarterly Journal of Mathematics},
  volume={17},
  number={1},
  pages={31--38},
  year={1966},
  publisher={Oxford University Press}
}

@article {AdamsPriddy,
    AUTHOR = {Adams, J. F. and Priddy, S. B.},
     TITLE = {Uniqueness of {$B{\rm SO}$}},
   JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
  FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
              Society},
    VOLUME = {80},
      YEAR = {1976},
    NUMBER = {3},
     PAGES = {475--509},
      ISSN = {0305-0041},
   MRCLASS = {55D35},
  MRNUMBER = {0431152},
MRREVIEWER = {V. P. Snaith},
       DOI = {10.1017/S0305004100053111},
       URL = {http://dx.doi.org/10.1017/S0305004100053111},
}

@article{Adem,
  title={The iteration of the Steenrod squares in algebraic topology},
  author={Adem, Jos{\'e}},
  journal={Proceedings of the National Academy of Sciences},
  volume={38},
  number={8},
  pages={720--726},
  year={1952},
  publisher={National Acad Sciences}
}

@article {Amitsur,
    AUTHOR = {Amitsur, S. A.},
     TITLE = {Simple algebras and cohomology groups of arbitrary fields},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {90},
      YEAR = {1959},
     PAGES = {73--112},
      ISSN = {0002-9947},
   MRCLASS = {18.00},
  MRNUMBER = {0101265},
MRREVIEWER = {D. Zelinsky},
       DOI = {10.2307/1993268},
       URL = {http://dx.doi.org/10.2307/1993268},
}

@article {ABP,
    AUTHOR = {Anderson, D. W. and Brown, Jr., E. H. and Peterson, F. P.},
     TITLE = {The structure of the {S}pin cobordism ring},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {86},
      YEAR = {1967},
     PAGES = {271--298},
      ISSN = {0003-486X},
   MRCLASS = {57.10},
  MRNUMBER = {0219077},
MRREVIEWER = {P. S. Landweber},
       DOI = {10.2307/1970690},
       URL = {http://dx.doi.org/10.2307/1970690},
}

@article {Ando,
    AUTHOR = {Ando, Matthew},
     TITLE = {Isogenies of formal group laws and power operations in the
              cohomology theories {$E_n$}},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {79},
      YEAR = {1995},
    NUMBER = {2},
     PAGES = {423--485},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {55N22 (14L05)},
  MRNUMBER = {1344767 (97a:55006)},
MRREVIEWER = {P. S. Landweber},
       DOI = {10.1215/S0012-7094-95-07911-3},
       URL = {http://dx.doi.org/10.1215/S0012-7094-95-07911-3},
}

@article {ABGHR,
    AUTHOR = {Ando, Matthew and Blumberg, Andrew J. and Gepner, David and
              Hopkins, Michael J. and Rezk, Charles},
     TITLE = {Units of ring spectra, orientations and {T}hom spectra via
              rigid infinite loop space theory},
   JOURNAL = {J. Topol.},
  FJOURNAL = {Journal of Topology},
    VOLUME = {7},
      YEAR = {2014},
    NUMBER = {4},
     PAGES = {1077--1117},
      ISSN = {1753-8416},
   MRCLASS = {55P43 (55N34 55R65)},
  MRNUMBER = {3286898},
MRREVIEWER = {Steven R. Costenoble},
       DOI = {10.1112/jtopol/jtu009},
       URL = {https://doi.org/10.1112/jtopol/jtu009},
}

@article {AFG,
    AUTHOR = {Ando, Matthew and French, Christopher P. and Ganter, Nora},
     TITLE = {The {J}acobi orientation and the two-variable elliptic genus},
   JOURNAL = {Algebr. Geom. Topol.},
  FJOURNAL = {Algebraic \& Geometric Topology},
    VOLUME = {8},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {493--539},
      ISSN = {1472-2747},
   MRCLASS = {55N34 (11F23 11F50 58J26)},
  MRNUMBER = {2443236},
MRREVIEWER = {Mark Hovey},
       DOI = {10.2140/agt.2008.8.493},
       URL = {http://dx.doi.org/10.2140/agt.2008.8.493},
}

@ARTICLE{AHR,
  author = {Ando, Matthew and Hopkins, Michael J. and Rezk, Charles},
  title = {Multiplicative orientations of $KO$--theory and the spectrum of topological modular forms},
  note = {\url{http://www.math.illinois.edu/~mando/papers/koandtmf.pdf}, Accessed: 2016-11-16}
}

@ARTICLE{AHRMoments,
  author = {Ando, Matthew and Hopkins, M. J. and Rezk, Charles},
  title = {Moments of {M}easures on {$\mathbb Z^\times_p$}, with {A}pplications to {M}aps between {$p$}--adic {$K$}--theory {S}pectra},
  note = {Unpublished}
}

@article {AHSHinfty,
    AUTHOR = {Ando, Matthew and Hopkins, Michael J. and Strickland, Neil P.},
     TITLE = {The sigma orientation is an {$H_\infty$} map},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {126},
      YEAR = {2004},
    NUMBER = {2},
     PAGES = {247--334},
      ISSN = {0002-9327},
     CODEN = {AJMAAN},
   MRCLASS = {55N34 (55P42 55P43)},
  MRNUMBER = {2045503 (2005d:55009)},
MRREVIEWER = {Paul G. Goerss},
       URL =
              {http://muse.jhu.edu/journals/american_journal_of_mathematics/v126/126.2ando.pdf},
}

@article {AHSTheoremOfTheCube,
    AUTHOR = {Ando, M. and Hopkins, M. J. and Strickland, N. P.},
     TITLE = {Elliptic spectra, the {W}itten genus and the theorem of the
              cube},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {146},
      YEAR = {2001},
    NUMBER = {3},
     PAGES = {595--687},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {55N34 (14H52 58J26)},
  MRNUMBER = {1869850 (2002g:55009)},
MRREVIEWER = {Mark Hovey},
       DOI = {10.1007/s002220100175},
       URL = {http://dx.doi.org/10.1007/s002220100175},
}

@incollection {AndoMorava,
    AUTHOR = {Ando, Matthew and Morava, Jack},
     TITLE = {A renormalized {R}iemann-{R}och formula and the {T}hom
              isomorphism for the free loop space},
 BOOKTITLE = {Topology, geometry, and algebra: interactions and new
              directions ({S}tanford, {CA}, 1999)},
    SERIES = {Contemp. Math.},
    VOLUME = {279},
     PAGES = {11--36},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2001},
   MRCLASS = {57R91 (14L05 19L10 55N20 55N34 58J26)},
  MRNUMBER = {1850739},
MRREVIEWER = {Neil P. Strickland},
       DOI = {10.1090/conm/279/04552},
       URL = {http://dx.doi.org/10.1090/conm/279/04552},
}

@article{AMS,
  title={Completions of {$\mathbb{Z}/(p)$}--Tate cohomology of periodic spectra},
  author={Ando, Matthew and Morava, Jack and Sadofsky, Hal},
  journal={Geometry \& Topology},
  volume={2},
  number={1},
  pages={145--174},
  year={1998},
  publisher={Mathematical Sciences Publishers}
}

@article {AndoStrickland,
    AUTHOR = {Ando, M. and Strickland, N. P.},
     TITLE = {Weil pairings and {M}orava {$K$}-theory},
   JOURNAL = {Topology},
  FJOURNAL = {Topology. An International Journal of Mathematics},
    VOLUME = {40},
      YEAR = {2001},
    NUMBER = {1},
     PAGES = {127--156},
      ISSN = {0040-9383},
     CODEN = {TPLGAF},
   MRCLASS = {55N22},
  MRNUMBER = {1791270 (2001i:55005)},
MRREVIEWER = {Mark Hovey},
       DOI = {10.1016/S0040-9383(99)00057-9},
       URL = {http://dx.doi.org/10.1016/S0040-9383(99)00057-9},
}

@article {AngeltveitLind,
    AUTHOR = {Angeltveit, Vigleik and Lind, John A.},
     TITLE = {Uniqueness of {$BP \langle n\rangle$}},
   JOURNAL = {J. Homotopy Relat. Struct.},
  FJOURNAL = {Journal of Homotopy and Related Structures},
    VOLUME = {12},
      YEAR = {2017},
    NUMBER = {1},
     PAGES = {17--30},
      ISSN = {2193-8407},
   MRCLASS = {55P42 (55S10)},
  MRNUMBER = {3613020},
MRREVIEWER = {Agn\`es Beaudry},
       URL = {https://doi.org/10.1007/s40062-015-0120-0},
}

@book {Araki,
    AUTHOR = {Araki, Sh\^or\^o},
     TITLE = {Typical formal groups in complex cobordism and {$K$}-theory},
      NOTE = {Lectures in Mathematics, Department of Mathematics, Kyoto
              University, No. 6},
 PUBLISHER = {Kinokuniya Book-Store Co., Ltd., Tokyo},
      YEAR = {1973},
     PAGES = {v+101 pp. (loose errata)},
   MRCLASS = {57D90 (55B15 14L05)},
  MRNUMBER = {0375354},
MRREVIEWER = {A. Dold},
}

@article {AtiyahSegalThm,
    AUTHOR = {Atiyah, M. F.},
     TITLE = {Characters and cohomology of finite groups},
   JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.},
  FJOURNAL = {Institut des Hautes \'Etudes Scientifiques. Publications
              Math\'ematiques},
    NUMBER = {9},
      YEAR = {1961},
     PAGES = {23--64},
      ISSN = {0073-8301},
   MRCLASS = {18.20},
  MRNUMBER = {0148722},
MRREVIEWER = {F. Hirzebruch},
       URL = {http://www.numdam.org/item?id=PMIHES_1961__9__23_0},
}

@article{Atiyah,
  title={Thom complexes},
  author={Atiyah, Michael Francis},
  journal={Proceedings of the London Mathematical Society},
  volume={3},
  number={1},
  pages={291--310},
  year={1961},
  publisher={Wiley Online Library}
}

@article {ABS,
    AUTHOR = {Atiyah, M. F. and Bott, R. and Shapiro, A.},
     TITLE = {Clifford modules},
   JOURNAL = {Topology},
  FJOURNAL = {Topology. An International Journal of Mathematics},
    VOLUME = {3},
      YEAR = {1964},
    NUMBER = {suppl. 1},
     PAGES = {3--38},
      ISSN = {0040-9383},
   MRCLASS = {57.30 (55.30)},
  MRNUMBER = {0167985},
MRREVIEWER = {J. F. Adams},
       DOI = {10.1016/0040-9383(64)90003-5},
       URL = {http://dx.doi.org/10.1016/0040-9383(64)90003-5},
}

@article{BaasMadsen,
  title={On the realization of certain modules over the Steenrod algebra},
  author={Baas, Nils Andreas and Madsen, Ib},
  journal={Mathematica Scandinavica},
  volume={31},
  number={1},
  pages={220--224},
  year={1973},
  publisher={JSTOR}
}

@article{BaezDolan,
  title={Euler characteristic versus homotopy cardinality},
  author={Baez, John},
  journal={Lecture at the Program on Applied Homotopy Theory, Fields Institute, Toronto, September},
  year={2003}
}

@article {BahriMahowald,
    AUTHOR = {Bahri, A. P. and Mahowald, M. E.},
     TITLE = {A direct summand in {$H^{\ast} (M{\rm O}\langle 8\rangle
              ,\,Z_{2})$}},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {78},
      YEAR = {1980},
    NUMBER = {2},
     PAGES = {295--298},
      ISSN = {0002-9939},
   MRCLASS = {57R90 (55S10)},
  MRNUMBER = {550517},
MRREVIEWER = {Vincent Giambalvo},
       URL = {https://doi.org/10.2307/2042276},
}

@incollection{BakerCombinatorialFGLs,
  title={Combinatorial and arithmetic identities based on formal group laws},
  author={Baker, Andrew},
  booktitle={Algebraic Topology Barcelona 1986},
  pages={17--34},
  year={1987},
  publisher={Springer}
}

@article {Baker,
    AUTHOR = {Baker, Andrew},
     TITLE = {Power operations and coactions in highly commutative homology
              theories},
   JOURNAL = {Publ. Res. Inst. Math. Sci.},
  FJOURNAL = {Publications of the Research Institute for Mathematical
              Sciences},
    VOLUME = {51},
      YEAR = {2015},
    NUMBER = {2},
     PAGES = {237--272},
      ISSN = {0034-5318},
   MRCLASS = {55S12 (55P43 55S10 55U35)},
  MRNUMBER = {3348109},
MRREVIEWER = {Geoffrey M. L. Powell},
       DOI = {10.4171/PRIMS/154},
       URL = {http://dx.doi.org/10.4171/PRIMS/154},
}

@article {BCGHRW,
    AUTHOR = {Baker, A. and Carlisle, D. and Gray, B. and Hilditch, S. and
              Ray, N. and Wood, R.},
     TITLE = {On the iterated complex transfer},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {199},
      YEAR = {1988},
    NUMBER = {2},
     PAGES = {191--207},
      ISSN = {0025-5874},
   MRCLASS = {55Q10 (55R12)},
  MRNUMBER = {958648},
MRREVIEWER = {Frederick Cohen},
       DOI = {10.1007/BF01159652},
       URL = {http://dx.doi.org/10.1007/BF01159652},
}

@article {Balmer,
    AUTHOR = {Balmer, Paul},
     TITLE = {Spectra, spectra, spectra---tensor triangular spectra versus
              {Z}ariski spectra of endomorphism rings},
   JOURNAL = {Algebr. Geom. Topol.},
  FJOURNAL = {Algebraic \& Geometric Topology},
    VOLUME = {10},
      YEAR = {2010},
    NUMBER = {3},
     PAGES = {1521--1563},
      ISSN = {1472-2747},
   MRCLASS = {18E30 (19K56 55U35)},
  MRNUMBER = {2661535 (2012a:18022)},
MRREVIEWER = {Amnon Neeman},
       DOI = {10.2140/agt.2010.10.1521},
       URL = {http://dx.doi.org/10.2140/agt.2010.10.1521},
}

@inproceedings{BPS,
  title={Unstable {A}dams Spectral Sequence Charts},
  author={Barnes, Dianne and Poduska, David and Shick, Paul},
  booktitle={Adams Memorial Symposium on Algebraic Topology: Manchester 1990},
  volume={2},
  pages={87},
  year={1992},
  organization={Cambridge University Press}
}

@ARTICLE{Barthel,
  author = {Barthel, Tobias},
  title = {Chromatic completion},
  note = {\url{http://people.mpim-bonn.mpg.de/tbarthel/CC.pdf}, Accessed: 2016-10-26}
}

@misc{BCSY,
      title={The Chromatic Fourier Transform}, 
      author={Tobias Barthel and Shachar Carmeli and Tomer M. Schlank and Lior Yanovski},
      year={2022},
      eprint={2210.12822},
      archivePrefix={arXiv},
      primaryClass={math.AT}
}

@article{BarthelFrankland,
author = "Barthel, Tobias and Frankland, Martin",
doi = "10.2140/agt.2015.15.2065",
fjournal = "Algebraic & Geometric Topology",
journal = "Algebr. Geom. Topol.",
number = "4",
pages = "2065--2131",
publisher = "MSP",
title = "Completed power operations for Morava $E$–theory",
url = "https://doi.org/10.2140/agt.2015.15.2065",
volume = "15",
year = "2015"
}

@ARTICLE{BSS,
   author = {{Barthel}, T. and {Schlank}, T. and {Stapleton}, N.},
    title = "{Chromatic homotopy theory is asymptotically algebraic}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1711.00844},
 primaryClass = "math.AT",
 keywords = {Mathematics - Algebraic Topology, Mathematics - Category Theory},
     year = 2017,
    month = nov,
   adsurl = {http://adsabs.harvard.edu/abs/2017arXiv171100844B},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article {BarthelStapleton,
    AUTHOR = {Barthel, Tobias and Stapleton, Nathaniel},
     TITLE = {The character of the total power operation},
   JOURNAL = {Geom. Topol.},
  FJOURNAL = {Geometry \& Topology},
    VOLUME = {21},
      YEAR = {2017},
    NUMBER = {1},
     PAGES = {385--440},
      ISSN = {1465-3060},
   MRCLASS = {55N22 (55P42 55S25)},
  MRNUMBER = {3608717},
       DOI = {10.2140/gt.2017.21.385},
       URL = {http://dx.doi.org/10.2140/gt.2017.21.385},
}

@article {Bauer,
    AUTHOR = {Bauer, Tilman},
     TITLE = {Formal plethories},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {254},
      YEAR = {2014},
     PAGES = {497--569},
      ISSN = {0001-8708},
   MRCLASS = {55S25 (16W99 18D20)},
  MRNUMBER = {3161106},
MRREVIEWER = {J. P. C. Greenlees},
       DOI = {10.1016/j.aim.2013.12.023},
       URL = {http://dx.doi.org/10.1016/j.aim.2013.12.023},
}

@ARTICLE{BauerTMF,
   author = {{Bauer}, T.},
    title = "{Computation of the homotopy of the spectrum tmf}",
  journal = {ArXiv Mathematics e-prints},
   eprint = {math/0311328},
 keywords = {Mathematics - Algebraic Topology, 55N34, 55T15},
     year = 2003,
    month = nov,
   adsurl = {http://adsabs.harvard.edu/abs/2003math.....11328B},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{Beaudry,
   author = {{Beaudry}, A.},
    title = "{The Chromatic Splitting Conjecture at $n=p=2$}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1502.02190},
 primaryClass = "math.AT",
 keywords = {Mathematics - Algebraic Topology, 55Q45, 55P60},
     year = 2015,
    month = feb,
   adsurl = {http://adsabs.harvard.edu/abs/2015arXiv150202190B},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article {Beardsley,
    AUTHOR = {Beardsley, Jonathan},
     TITLE = {A theorem on multiplicative cell attachments with an
              application to {R}avenel's {$X(n)$} spectra},
   JOURNAL = {J. Homotopy Relat. Struct.},
  FJOURNAL = {Journal of Homotopy and Related Structures},
    VOLUME = {14},
      YEAR = {2019},
    NUMBER = {3},
     PAGES = {611--624},
      ISSN = {2193-8407},
   MRCLASS = {55P42 (55N22 55P48)},
  MRNUMBER = {3987551},
       DOI = {10.1007/s40062-018-0222-6},
       URL = {https://doi.org/10.1007/s40062-018-0222-6},
}

@article {BehrensBuildings,
    AUTHOR = {Behrens, Mark},
     TITLE = {Buildings, elliptic curves, and the {$K(2)$}-local sphere},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {129},
      YEAR = {2007},
    NUMBER = {6},
     PAGES = {1513--1563},
      ISSN = {0002-9327},
     CODEN = {AJMAAN},
   MRCLASS = {55Q52 (11F23 20E42 55N22 55Q40)},
  MRNUMBER = {2369888},
MRREVIEWER = {Tyler D. Lawson},
       DOI = {10.1353/ajm.2007.0037},
       URL = {http://dx.doi.org/10.1353/ajm.2007.0037},
}

@article {BehrensCongruences,
    AUTHOR = {Behrens, Mark},
     TITLE = {Congruences between modular forms given by the divided
              {$\beta$} family in homotopy theory},
   JOURNAL = {Geom. Topol.},
  FJOURNAL = {Geometry \& Topology},
    VOLUME = {13},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {319--357},
      ISSN = {1465-3060},
   MRCLASS = {55Q45 (11F23 11F33 55N34 55Q51 55T15)},
  MRNUMBER = {2469520},
MRREVIEWER = {Tyler D. Lawson},
       DOI = {10.2140/gt.2009.13.319},
       URL = {http://dx.doi.org/10.2140/gt.2009.13.319},
}

@incollection {BehrensConstruction,
    AUTHOR = {Behrens, Mark},
     TITLE = {The construction of {$\mathit{tmf}$}},
 BOOKTITLE = {Topological Modular Forms},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {201},
     PAGES = {149--206},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2014},
}

@article {BehrensGoodwillie,
    AUTHOR = {Behrens, Mark},
     TITLE = {The {G}oodwillie tower and the {EHP} sequence},
   JOURNAL = {Mem. Amer. Math. Soc.},
  FJOURNAL = {Memoirs of the American Mathematical Society},
    VOLUME = {218},
      YEAR = {2012},
    NUMBER = {1026},
     PAGES = {xii+90},
      ISSN = {0065-9266},
      ISBN = {978-0-8218-6902-4},
   MRCLASS = {55Q40 (55Q10 55Q15)},
  MRNUMBER = {2976788},
MRREVIEWER = {Gregory Z. Arone},
       DOI = {10.1090/S0065-9266-2011-00645-3},
       URL = {http://dx.doi.org/10.1090/S0065-9266-2011-00645-3},
}

@article {BehrensModularDescription,
    AUTHOR = {Behrens, Mark},
     TITLE = {A modular description of the {$K(2)$}-local sphere at the
              prime 3},
   JOURNAL = {Topology},
  FJOURNAL = {Topology. An International Journal of Mathematics},
    VOLUME = {45},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {343--402},
      ISSN = {0040-9383},
     CODEN = {TPLGAF},
   MRCLASS = {55Q40 (11F23 14H52 55N34 55Q51 55S05)},
  MRNUMBER = {2193339},
MRREVIEWER = {Mark Hovey},
       DOI = {10.1016/j.top.2005.08.005},
       URL = {http://dx.doi.org/10.1016/j.top.2005.08.005},
}

@article {BehrensRevisited,
    AUTHOR = {Behrens, Mark},
     TITLE = {The homotopy groups of {$S_{E(2)}$} at {$p\geq 5$}
              revisited},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {230},
      YEAR = {2012},
    NUMBER = {2},
     PAGES = {458--492},
      ISSN = {0001-8708},
     CODEN = {ADMTA4},
   MRCLASS = {55Q45 (55T15)},
  MRNUMBER = {2914955},
MRREVIEWER = {Paul G. Goerss},
       DOI = {10.1016/j.aim.2012.02.023},
       URL = {http://dx.doi.org/10.1016/j.aim.2012.02.023},
}

@article{BehrensRootInv,
  title={Root invariants in the Adams spectral sequence},
  author={Behrens, Mark},
  journal={Transactions of the American Mathematical Society},
  volume={358},
  number={10},
  pages={4279--4341},
  year={2006}
}

@article{BehrensLaures,
  title={{$\beta$}--family congruences and the {$f$}--invariant},
  author={Behrens, Mark and Laures, Gerd},
  journal={Geometry \& Topology Monographs},
  volume={16},
  pages={9--29},
  year={2009}
}

@article {BehrensLawson,
    AUTHOR = {Behrens, Mark and Lawson, Tyler},
     TITLE = {Topological automorphic forms},
   JOURNAL = {Mem. Amer. Math. Soc.},
  FJOURNAL = {Memoirs of the American Mathematical Society},
    VOLUME = {204},
      YEAR = {2010},
    NUMBER = {958},
     PAGES = {xxiv+141},
      ISSN = {0065-9266},
      ISBN = {978-0-8218-4539-4},
   MRCLASS = {55N34 (11F23 14G35 55N22 55P43)},
  MRNUMBER = {2640996},
MRREVIEWER = {Paul G. Goerss},
       DOI = {10.1090/S0065-9266-09-00573-0},
       URL = {http://dx.doi.org/10.1090/S0065-9266-09-00573-0},
}

@article{BeilinsonAdeles,
  title={Residues and adeles},
  author={Beilinson, Aleksandr Aleksandrovich},
  journal={Functional Analysis and Its Applications},
  volume={14},
  number={1},
  pages={34--35},
  year={1980},
  publisher={Springer}
}

@book {BeilinsonDrinfeld,
    AUTHOR = {Beilinson, A. A. and Drinfeld, V.},
     TITLE = {Quantization of {H}itchin's integrable system and {H}ecke eigensheaves},
      NOTE = {Preprint available online at {http://www.math.uchicago.edu/{\textasciitilde}mitya/langlands/hitchin/BD-hitchin.pdf}},
}

@article {BCM,
    AUTHOR = {Bendersky, M. and Curtis, E. B. and Miller, H. R.},
     TITLE = {The unstable {A}dams spectral sequence for generalized
              homology},
   JOURNAL = {Topology},
  FJOURNAL = {Topology. An International Journal of Mathematics},
    VOLUME = {17},
      YEAR = {1978},
    NUMBER = {3},
     PAGES = {229--248},
      ISSN = {0040-9383},
     CODEN = {TPLGAF},
   MRCLASS = {55T15},
  MRNUMBER = {508887 (80g:55035)},
MRREVIEWER = {Stanley Kochman},
       DOI = {10.1016/0040-9383(78)90028-9},
       URL = {http://dx.doi.org/10.1016/0040-9383(78)90028-9},
}

@misc{BlomquistHarper,
Author = {Jacobson R. Blomquist and John E. Harper},
Title = {An integral chains analog of Quillen's rational homotopy theory equivalence},
Year = {2016},
Eprint = {arXiv:1611.04157},
}

@incollection {BoardmanConditionallyConvergent,
    AUTHOR = {Boardman, J. Michael},
     TITLE = {Conditionally convergent spectral sequences},
 BOOKTITLE = {Homotopy invariant algebraic structures ({B}altimore, {MD},
              1998)},
    SERIES = {Contemp. Math.},
    VOLUME = {239},
     PAGES = {49--84},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1999},
   MRCLASS = {55T05 (18A30 18G40)},
  MRNUMBER = {1718076},
MRREVIEWER = {John McCleary},
       URL = {https://doi.org/10.1090/conm/239/03597},
}

@incollection {BoardmanEightfoldWay,
    AUTHOR = {Boardman, J. M.},
     TITLE = {The eightfold way to {BP}-operations or {$E\sb\ast E$}\ and
              all that},
 BOOKTITLE = {Current trends in algebraic topology, {P}art 1 ({L}ondon,
              {O}nt., 1981)},
    SERIES = {CMS Conf. Proc.},
    VOLUME = {2},
     PAGES = {187--226},
 PUBLISHER = {Amer. Math. Soc., Providence, R.I.},
      YEAR = {1982},
   MRCLASS = {55N20 (55S05)},
  MRNUMBER = {686116},
MRREVIEWER = {J. F. Adams},
}

@inproceedings {BordismSplitting,
    AUTHOR = {Boardman, J. M.},
     TITLE = {Splitting of {$M{\rm U}$} and other spectra},
 BOOKTITLE = {Geometric applications of homotopy theory ({P}roc. {C}onf.,
              {E}vanston, {I}ll., 1977), {II}},
    SERIES = {Lecture Notes in Math.},
    VOLUME = {658},
     PAGES = {27--79},
 PUBLISHER = {Springer, Berlin},
      YEAR = {1978},
   MRCLASS = {55N20},
  MRNUMBER = {513568},
MRREVIEWER = {J. P. May},
}

@incollection {BJW,
    AUTHOR = {Boardman, J. Michael and Johnson, David Copeland and Wilson,
              W. Stephen},
     TITLE = {Unstable operations in generalized cohomology},
 BOOKTITLE = {Handbook of algebraic topology},
     PAGES = {687--828},
 PUBLISHER = {North-Holland, Amsterdam},
      YEAR = {1995},
   MRCLASS = {55S25 (55N20)},
  MRNUMBER = {1361900 (97b:55022)},
MRREVIEWER = {Haynes R. Miller},
       DOI = {10.1016/B978-044481779-2/50016-X},
       URL = {http://dx.doi.org/10.1016/B978-044481779-2/50016-X},
}

@article {BousfieldLambdaRings,
    AUTHOR = {Bousfield, A. K.},
     TITLE = {On {$\lambda$}-rings and the {$K$}-theory of infinite loop
              spaces},
   JOURNAL = {$K$-Theory},
  FJOURNAL = {$K$-Theory. An Interdisciplinary Journal for the Development,
              Application, and Influence of $K$-Theory in the Mathematical
              Sciences},
    VOLUME = {10},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {1--30},
      ISSN = {0920-3036},
   MRCLASS = {55N15 (19L20 55P47 55S25)},
  MRNUMBER = {1373816},
MRREVIEWER = {Robert D. Thompson},
       DOI = {10.1007/BF00534886},
       URL = {http://dx.doi.org/10.1007/BF00534886},
}

@article {BousfieldLocalization,
    AUTHOR = {Bousfield, A. K.},
     TITLE = {The localization of spectra with respect to homology},
   JOURNAL = {Topology},
  FJOURNAL = {Topology. An International Journal of Mathematics},
    VOLUME = {18},
      YEAR = {1979},
    NUMBER = {4},
     PAGES = {257--281},
      ISSN = {0040-9383},
     CODEN = {TPLGAF},
   MRCLASS = {55N20 (55N15 55P60)},
  MRNUMBER = {551009},
MRREVIEWER = {Willi Meier},
       DOI = {10.1016/0040-9383(79)90018-1},
       URL = {http://dx.doi.org/10.1016/0040-9383(79)90018-1},
}

@article {BousfieldUnstableLocalization,
    AUTHOR = {Bousfield, A. K.},
     TITLE = {The localization of spaces with respect to homology},
   JOURNAL = {Topology},
  FJOURNAL = {Topology. An International Journal of Mathematics},
    VOLUME = {14},
      YEAR = {1975},
     PAGES = {133--150},
      ISSN = {0040-9383},
   MRCLASS = {55D05},
  MRNUMBER = {0380779},
MRREVIEWER = {M. Mimura},
       DOI = {10.1016/0040-9383(75)90023-3},
       URL = {http://dx.doi.org/10.1016/0040-9383(75)90023-3},
}

@book {Breen,
    AUTHOR = {Breen, Lawrence},
     TITLE = {Fonctions th\^eta et th\'eor\`eme du cube},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {980},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {1983},
     PAGES = {xiii+115},
      ISBN = {3-540-12002-5},
   MRCLASS = {14K25},
  MRNUMBER = {823233},
MRREVIEWER = {N. Yui},
}

@article {Browder,
    AUTHOR = {Browder, William},
     TITLE = {The {K}ervaire invariant of framed manifolds and its
              generalization},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {90},
      YEAR = {1969},
     PAGES = {157--186},
      ISSN = {0003-486X},
   MRCLASS = {57.10},
  MRNUMBER = {0251736},
MRREVIEWER = {Edgar H. Brown, Jr.},
       DOI = {10.2307/1970686},
       URL = {http://dx.doi.org/10.2307/1970686},
}


@book {BMMS,
    AUTHOR = {Bruner, R. R. and May, J. P. and McClure, J. E. and
              Steinberger, M.},
     TITLE = {{$H_\infty $} ring spectra and their applications},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {1176},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {1986},
     PAGES = {viii+388},
      ISBN = {3-540-16434-0},
   MRCLASS = {55-02 (55P42 55Sxx)},
  MRNUMBER = {836132},
MRREVIEWER = {Haynes R. Miller},
       DOI = {10.1007/BFb0075405},
       URL = {http://dx.doi.org/10.1007/BFb0075405},
}

@article {BuchstaberLazarev,
    AUTHOR = {Buchstaber, Victor and Lazarev, Andrey},
     TITLE = {Dieudonn\'e modules and {$p$}-divisible groups associated with
              {M}orava {$K$}-theory of {E}ilenberg-{M}ac {L}ane spaces},
   JOURNAL = {Algebr. Geom. Topol.},
  FJOURNAL = {Algebraic \& Geometric Topology},
    VOLUME = {7},
      YEAR = {2007},
     PAGES = {529--564},
      ISSN = {1472-2747},
   MRCLASS = {55N22 (14L05)},
  MRNUMBER = {2308956 (2008e:55004)},
MRREVIEWER = {Mark Hovey},
       DOI = {10.2140/agt.2007.7.529},
       URL = {http://dx.doi.org/10.2140/agt.2007.7.529},
}

@article {BullettMacdonald,
    AUTHOR = {Bullett, S. R. and Macdonald, I. G.},
     TITLE = {On the {A}dem relations},
   JOURNAL = {Topology},
  FJOURNAL = {Topology. An International Journal of Mathematics},
    VOLUME = {21},
      YEAR = {1982},
    NUMBER = {3},
     PAGES = {329--332},
      ISSN = {0040-9383},
   MRCLASS = {55S05 (55S10)},
  MRNUMBER = {649764},
MRREVIEWER = {Frederick Cohen},
       DOI = {10.1016/0040-9383(82)90015-5},
       URL = {https://doi.org/10.1016/0040-9383(82)90015-5},
}

@article {ButowiezTurner,
    AUTHOR = {Butowiez, Jean-Yves and Turner, Paul},
     TITLE = {Unstable multiplicative cohomology operations},
   JOURNAL = {Q. J. Math.},
  FJOURNAL = {The Quarterly Journal of Mathematics},
    VOLUME = {51},
      YEAR = {2000},
    NUMBER = {4},
     PAGES = {437--449},
      ISSN = {0033-5606},
   MRCLASS = {55S25},
  MRNUMBER = {1806451},
MRREVIEWER = {Donald M. Davis},
       DOI = {10.1093/qjmath/51.4.437},
       URL = {http://dx.doi.org/10.1093/qjmath/51.4.437},
}

@inproceedings{Cartier,
  title={Quantum mechanical commutation relations and theta functions},
  author={Cartier, Pierre},
  booktitle={Proc. Sympos. Pure Math},
  volume={9},
  pages={361--383},
  year={1966}
}

@book {CCO,
    AUTHOR = {Chai, Ching-Li and Conrad, Brian and Oort, Frans},
     TITLE = {Complex multiplication and lifting problems},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {195},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2014},
     PAGES = {x+387},
      ISBN = {978-1-4704-1014-8},
   MRCLASS = {14K22 (11G15 14D15 14K02 14K15 14L05)},
  MRNUMBER = {3137398},
MRREVIEWER = {Mihran Papikian},
}

@article {Chan,
    AUTHOR = {Chan, Ken},
     TITLE = {A simple proof that the unstable (co)-homology of the
              {B}rown-{P}eterson spectrum is torsion free},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {26},
      YEAR = {1982},
    NUMBER = {2},
     PAGES = {155--157},
      ISSN = {0022-4049},
   MRCLASS = {55N20 (55T99)},
  MRNUMBER = {675011},
MRREVIEWER = {Edgar H. Brown, Jr.},
       DOI = {10.1016/0022-4049(82)90020-2},
       URL = {http://dx.doi.org/10.1016/0022-4049(82)90020-2},
}

@article{ClausenMathew,
  title={A short proof of telescopic Tate vanishing},
  author={Clausen, Dustin and Mathew, Akhil},
  journal={Proceedings of the American Mathematical Society},
  volume={145},
  number={12},
  pages={5413--5417},
  year={2017}
}

@article {Cohen,
    AUTHOR = {Cohen, Ralph L.},
     TITLE = {Odd primary infinite families in stable homotopy theory},
   JOURNAL = {Mem. Amer. Math. Soc.},
  FJOURNAL = {Memoirs of the American Mathematical Society},
    VOLUME = {30},
      YEAR = {1981},
    NUMBER = {242},
     PAGES = {viii+92},
      ISSN = {0065-9266},
   MRCLASS = {55Q45 (55T15)},
  MRNUMBER = {603393},
MRREVIEWER = {J. F. Adams},
       URL = {https://doi.org/10.1090/memo/0242},
}

@book {ConnerFloyd,
    AUTHOR = {Conner, P. E. and Floyd, E. E.},
     TITLE = {The relation of cobordism to {$K$}-theories},
    SERIES = {Lecture Notes in Mathematics, No. 28},
 PUBLISHER = {Springer-Verlag, Berlin-New York},
      YEAR = {1966},
     PAGES = {v+112},
   MRCLASS = {57.10 (55.00)},
  MRNUMBER = {0216511},
MRREVIEWER = {M. F. Atiyah},
}

@book {ConnerFloydBook,
    AUTHOR = {Conner, P. E. and Floyd, E. E.},
     TITLE = {Differentiable periodic maps},
    SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Band
              33},
 PUBLISHER = {Academic Press Inc., Publishers, New York; Springer-Verlag,
              Berlin-G\"{o}ttingen-Heidelberg},
      YEAR = {1964},
     PAGES = {vii+148},
   MRCLASS = {57.10 (55.36)},
  MRNUMBER = {0176478},
MRREVIEWER = {E. Dyer},
}

@incollection {Davis,
    AUTHOR = {Davis, Donald M.},
     TITLE = {Computing {$v_1$}-periodic homotopy groups of spheres and some
              compact {L}ie groups},
 BOOKTITLE = {Handbook of algebraic topology},
     PAGES = {993--1048},
 PUBLISHER = {North-Holland, Amsterdam},
      YEAR = {1995},
   MRCLASS = {55Q40 (55Q52 57T20)},
  MRNUMBER = {1361905},
MRREVIEWER = {Robert D. Thompson},
       DOI = {10.1016/B978-044481779-2/50021-3},
       URL = {http://dx.doi.org/10.1016/B978-044481779-2/50021-3},
}

@article {DavisLawson,
    AUTHOR = {Davis, Daniel G. and Lawson, Tyler},
     TITLE = {Commutative ring objects in pro-categories and generalized
              {M}oore spectra},
   JOURNAL = {Geom. Topol.},
  FJOURNAL = {Geometry \& Topology},
    VOLUME = {18},
      YEAR = {2014},
    NUMBER = {1},
     PAGES = {103--140},
      ISSN = {1465-3060},
   MRCLASS = {55P43 (18D20 18D50 18G55 55U35)},
  MRNUMBER = {3158773},
MRREVIEWER = {Julia Bergner},
       DOI = {10.2140/gt.2014.18.103},
       URL = {http://dx.doi.org/10.2140/gt.2014.18.103},
}

@article {DavisMahowald,
    AUTHOR = {Davis, Donald M. and Mahowald, Mark},
     TITLE = {The nonrealizability of the quotient {$A//A_{2}$}\ of the
              {S}teenrod algebra},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {104},
      YEAR = {1982},
    NUMBER = {6},
     PAGES = {1211--1216},
      ISSN = {0002-9327},
   MRCLASS = {55P42},
  MRNUMBER = {681734},
MRREVIEWER = {J. F. Adams},
       URL = {https://doi.org/10.2307/2374058},
}

@book {Demazure,
    AUTHOR = {Demazure, Michel},
     TITLE = {Lectures on {$p$}-divisible groups},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {302},
      NOTE = {Reprint of the 1972 original},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1986},
     PAGES = {vi+98},
      ISBN = {3-540-06092-8},
   MRCLASS = {14L05 (11G10)},
  MRNUMBER = {883960 (88a:14049)},
}

@book {DemazureGabriel,
    AUTHOR = {Demazure, Michel and Gabriel, Pierre},
     TITLE = {Groupes alg\'ebriques. {T}ome {I}: {G}\'eom\'etrie alg\'ebrique,
              g\'en\'eralit\'es, groupes commutatifs},
      NOTE = {Avec un appendice {{\i}t Corps de classes local} par Michiel
              Hazewinkel},
 PUBLISHER = {Masson \& Cie, \'Editeur, Paris; North-Holland Publishing Co.,
              Amsterdam},
      YEAR = {1970},
     PAGES = {xxvi+700},
   MRCLASS = {14L15 (20G35)},
  MRNUMBER = {0302656},
MRREVIEWER = {J.-E. Bertin},
}

@incollection {Dessai,
    AUTHOR = {Dessai, Anand},
     TITLE = {Some geometric properties of the {W}itten genus},
 BOOKTITLE = {Alpine perspectives on algebraic topology},
    SERIES = {Contemp. Math.},
    VOLUME = {504},
     PAGES = {99--115},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2009},
   MRCLASS = {58J26 (57R20 57S15)},
  MRNUMBER = {2581907},
       DOI = {10.1090/conm/504/09877},
       URL = {https://doi.org/10.1090/conm/504/09877},
}

@article{Devalapurkar,
  title={Roots of unity in {$K(n)$}--local {$E_\infty$}-rings},
  author={Devalapurkar, Sanath K},
  journal={arXiv preprint arXiv:1707.09957},
  year={2017}
}

@article {DevinatzHopkins,
    AUTHOR = {Devinatz, Ethan S. and Hopkins, Michael J.},
     TITLE = {The action of the {M}orava stabilizer group on the
              {L}ubin-{T}ate moduli space of lifts},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {117},
      YEAR = {1995},
    NUMBER = {3},
     PAGES = {669--710},
      ISSN = {0002-9327},
     CODEN = {AJMAAN},
   MRCLASS = {55N22 (14L05 55P42 55Q45)},
  MRNUMBER = {1333942},
MRREVIEWER = {Andrew J. Baker},
       DOI = {10.2307/2375086},
       URL = {http://dx.doi.org/10.2307/2375086},
}

@article {DHS,
    AUTHOR = {Devinatz, Ethan S. and Hopkins, Michael J. and Smith, Jeffrey
              H.},
     TITLE = {Nilpotence and stable homotopy theory. {I}},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {128},
      YEAR = {1988},
    NUMBER = {2},
     PAGES = {207--241},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {55Q10 (55P42 55Q52)},
  MRNUMBER = {960945 (89m:55009)},
MRREVIEWER = {Frederick Cohen},
       DOI = {10.2307/1971440},
       URL = {http://dx.doi.org/10.2307/1971440},
}

@article{Dicke,
author = {H. Dicke, R},
year = {1990},
month = {01},
pages = {121-},
title = {Dirac's Cosmology and Mach's Principle},
volume = {192},
booktitle = {Physical Cosmology and Philosophy}
}

@incollection {DouglasHenriques,
    AUTHOR = {Douglas, Christopher L. and Henriques, Andr\'e G.},
     TITLE = {Topological modular forms and conformal nets},
 BOOKTITLE = {Mathematical foundations of quantum field theory and
              perturbative string theory},
    SERIES = {Proc. Sympos. Pure Math.},
    VOLUME = {83},
     PAGES = {341--354},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2011},
   MRCLASS = {81T05 (18D05 19D99 55N34 81T40)},
  MRNUMBER = {2742433},
MRREVIEWER = {Mark J. Behrens},
       DOI = {10.1090/pspum/083/2742433},
       URL = {http://dx.doi.org/10.1090/pspum/083/2742433},
}


@preamble{
   "\def\cprime{$'$} "
}
@article {Drinfeld,
    AUTHOR = {Drinfel{\cprime}d, V. G.},
     TITLE = {Elliptic modules},
   JOURNAL = {Mat. Sb. (N.S.)},
    VOLUME = {94(136)},
      YEAR = {1974},
     PAGES = {594--627, 656},
   MRCLASS = {10D99 (14K15)},
  MRNUMBER = {0384707},
MRREVIEWER = {Pierre Deligne},
}

@book {EKMM,
    AUTHOR = {Elmendorf, A. D. and Kriz, I. and Mandell, M. A. and May, J.
              P.},
     TITLE = {Rings, modules, and algebras in stable homotopy theory},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {47},
      NOTE = {With an appendix by M. Cole},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {1997},
     PAGES = {xii+249},
      ISBN = {0-8218-0638-6},
   MRCLASS = {55N20 (19D10 19D55 55P42 55T25)},
  MRNUMBER = {1417719 (97h:55006)},
MRREVIEWER = {Donald M. Davis},
}

@article{Fox,
title = "The construction of cofree coalgebras",
journal = "Journal of Pure and Applied Algebra",
volume = "84",
number = "2",
pages = "191 - 198",
year = "1993",
issn = "0022-4049",
doi = "https://doi.org/10.1016/0022-4049(93)90038-U",
url = "http://www.sciencedirect.com/science/article/pii/002240499390038U",
author = "Thomas F. Fox"
}

@article{GanterPowerOpnsInTateKthy,
  title={Power operations in orbifold Tate $ K $-theory},
  author={Ganter, Nora and others},
  journal={Homology, Homotopy and Applications},
  volume={15},
  number={1},
  pages={313--342},
  year={2013},
  publisher={International Press of Boston}
}

@ARTICLE{GanterStringyOpns,
   author = {{Ganter}, N.},
    title = "{Stringy power operations in Tate K-theory}",
  journal = {ArXiv Mathematics e-prints},
   eprint = {math/0701565},
 keywords = {Mathematics - Algebraic Topology, Mathematical Physics, 55N34, 55P35, 58J26},
     year = 2007,
    month = jan,
   adsurl = {http://adsabs.harvard.edu/abs/2007math......1565G},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@inproceedings{GiambalvoPengelley,
  title={The homology of {$M\mathit{Spin}$}},
  author={Giambalvo, Vincent and Pengelley, David J},
  booktitle={Mathematical Proceedings of the Cambridge Philosophical Society},
  volume={95},
  number={3},
  pages={427--436},
  year={1984},
  organization={Cambridge University Press}
}

@article{GKV,
  title={Elliptic algebras and equivariant elliptic cohomology},
  author={Ginzburg, Victor and Kapranov, Mikhail and Vasserot, Eric},
  journal={arXiv preprint q-alg/9505012},
  year={1995}
}

@article {GoerssChains,
    AUTHOR = {Goerss, Paul G.},
     TITLE = {Simplicial chains over a field and {$p$}-local homotopy
              theory},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {220},
      YEAR = {1995},
    NUMBER = {4},
     PAGES = {523--544},
      ISSN = {0025-5874},
   MRCLASS = {55P15 (18D15 55P60)},
  MRNUMBER = {1363853},
MRREVIEWER = {Richard John Steiner},
       DOI = {10.1007/BF02572629},
       URL = {https://doi.org/10.1007/BF02572629},
}

@incollection {GoerssDieudonne,
    AUTHOR = {Goerss, Paul G.},
     TITLE = {Hopf rings, {D}ieudonn\'e modules, and {$E_*\Omega^2S^3$}},
 BOOKTITLE = {Homotopy invariant algebraic structures ({B}altimore, {MD},
              1998)},
    SERIES = {Contemp. Math.},
    VOLUME = {239},
     PAGES = {115--174},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1999},
   MRCLASS = {57T05 (16W30 55N20 55P35 55S05)},
  MRNUMBER = {1718079 (2000j:57078)},
MRREVIEWER = {Neil P. Strickland},
       DOI = {10.1090/conm/239/03600},
       URL = {http://dx.doi.org/10.1090/conm/239/03600},
}

@article{GoerssQCohOnMfg,
  author = {Goerss, Paul G.},
  title = {Quasi-coherent sheaves on the moduli stack of formal groups},
  archivePrefix = "arXiv",
  eprint = {0802.0996},
  primaryClass = "math.AT",
  year = {2008}
}

@article{GoerssRealizingFamilies,
  title={Realizing families of Landweber exact homology theories},
  author={Goerss, Paul G},
  journal={New topological contexts for Galois theory and algebraic geometry (BIRS 2008)},
  volume={16},
  pages={49--78},
  year={2009}
}

@article {GoerssTMF,
    AUTHOR = {Goerss, Paul G.},
     TITLE = {Topological modular forms [after {H}opkins, {M}iller and
              {L}urie]},
      NOTE = {S\'eminaire Bourbaki. Volume 2008/2009. Expos\'es 997--1011},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {332},
      YEAR = {2010},
     PAGES = {Exp. No. 1005, viii, 221--255},
      ISSN = {0303-1179},
      ISBN = {978-2-85629-291-4},
   MRCLASS = {55N34 (11F23 14D23 14H52 14L05 55N22)},
  MRNUMBER = {2648680},
MRREVIEWER = {Tyler D. Lawson},
}

@incollection {GoerssHopkins,
    AUTHOR = {Goerss, P. G. and Hopkins, M. J.},
     TITLE = {Moduli spaces of commutative ring spectra},
 BOOKTITLE = {Structured ring spectra},
    SERIES = {London Math. Soc. Lecture Note Ser.},
    VOLUME = {315},
     PAGES = {151--200},
 PUBLISHER = {Cambridge Univ. Press, Cambridge},
      YEAR = {2004},
   MRCLASS = {55P43},
  MRNUMBER = {2125040},
MRREVIEWER = {Birgit Richter},
       DOI = {10.1017/CBO9780511529955.009},
       URL = {http://dx.doi.org/10.1017/CBO9780511529955.009},
}

@incollection {GLM,
    AUTHOR = {Goerss, P. and Lannes, J. and Morel, F.},
     TITLE = {Hopf algebras, {W}itt vectors, and {B}rown-{G}itler spectra},
 BOOKTITLE = {Algebraic topology ({O}axtepec, 1991)},
    SERIES = {Contemp. Math.},
    VOLUME = {146},
     PAGES = {111--128},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1993},
   MRCLASS = {55N20 (16W30 55P42 55P47)},
  MRNUMBER = {1224910 (95a:55007)},
       DOI = {10.1090/conm/146/01218},
       URL = {http://dx.doi.org/10.1090/conm/146/01218},
}

@article{Gonzalez,
  title={A vanishing line in the {$BP \langle 1 \rangle$}-Adams spectral sequence},
  author={Gonz{\'a}lez, Jes{\'u}s},
  journal={Topology},
  volume={39},
  number={6},
  pages={1137--1153},
  year={2000},
  publisher={Elsevier}
}

@book{GreenleesMay,
  title={Generalized Tate cohomology},
  author={Greenlees, John Patrick Campbell and May, J Peter},
  volume={543},
  year={1995},
  publisher={American Mathematical Soc.}
}

@Article{GreenleesSadofsky,
author={Greenlees, J. P. C. and Sadofsky, Hal},
title={The Tate spectrum of {$v_n$}-periodic complex oriented theories},
journal={Mathematische Zeitschrift},
year={1996},
month={Jul},
day={01},
volume={222},
number={3},
pages={391--405},
issn={1432-1823},
doi={10.1007/BF02621873},
url={https://doi.org/10.1007/BF02621873}
}

@article{GreenleesStrickland,
  title={Varieties and local cohomology for chromatic group cohomology rings},
  author={Greenlees, JPC and Strickland, NP},
  journal={Topology},
  volume={38},
  number={5},
  pages={1093--1139},
  year={1999},
  publisher={Elsevier}
}

@misc{Gregoric,
  doi = {10.48550/ARXIV.2107.08657},
  
  url = {https://arxiv.org/abs/2107.08657},
  
  author = {Gregoric, Rok},
  
  keywords = {Algebraic Geometry (math.AG), Algebraic Topology (math.AT), FOS: Mathematics, FOS: Mathematics, 14A30, 55N22, 55P43},
  
  title = {Moduli stack of oriented formal groups and periodic complex bordism},
  
  publisher = {arXiv},
  
  year = {2021},
  
  copyright = {arXiv.org perpetual, non-exclusive license}
}

@incollection {Grojnowski,
    AUTHOR = {Grojnowski, I.},
     TITLE = {Delocalised equivariant elliptic cohomology},
 BOOKTITLE = {Elliptic cohomology},
    SERIES = {London Math. Soc. Lecture Note Ser.},
    VOLUME = {342},
     PAGES = {114--121},
 PUBLISHER = {Cambridge Univ. Press, Cambridge},
      YEAR = {2007},
   MRCLASS = {55N34 (20G05 55N91)},
  MRNUMBER = {2330510},
MRREVIEWER = {J. P. C. Greenlees},
       DOI = {10.1017/CBO9780511721489.007},
       URL = {http://dx.doi.org/10.1017/CBO9780511721489.007},
}

@article{Gross,
  title={On canonical and quasi-canonical liftings},
  author={Gross, Benedict H},
  journal={Inventiones mathematicae},
  volume={84},
  number={2},
  pages={321--326},
  year={1986},
  publisher={Springer}
}

@book {GrothendieckCristaux,
    AUTHOR = {Grothendieck, Alexandre},
     TITLE = {Groupes de {B}arsotti-{T}ate et cristaux de {D}ieudonn\'e},
      NOTE = {S\'eminaire de Math\'ematiques Sup\'erieures, No. 45 (\'Et\'e, 1970)},
 PUBLISHER = {Les Presses de l'Universit\'e de Montr\'eal, Montreal, Que.},
      YEAR = {1974},
     PAGES = {155},
   MRCLASS = {14L05 (14F30)},
  MRNUMBER = {0417192},
MRREVIEWER = {Robert A. Morris},
}

@article{GrothendieckSGAI,
  title={Rev{\^e}tement {\'e}tales et groupe fondamental (SGA1)},
  author={Grothendieck, Alexandre},
  journal={Lecture Notes in Math.},
  volume={288},
  year={1971},
  publisher={Springer}
}

@article{HahnMitchell,
  title={Iwasawa theory for {$K(1)$}-local spectra},
  author={Hahn, Rebekah and Mitchell, Stephen},
  journal={Transactions of the American Mathematical Society},
  volume={359},
  number={11},
  pages={5207--5238},
  year={2007}
}

@article {Harris,
    AUTHOR = {Harris, Bruno},
     TITLE = {Bott periodicity via simplicial spaces},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {62},
      YEAR = {1980},
    NUMBER = {2},
     PAGES = {450--454},
      ISSN = {0021-8693},
     CODEN = {JALGA4},
   MRCLASS = {55R45},
  MRNUMBER = {563240},
MRREVIEWER = {Harold Hastings},
       DOI = {10.1016/0021-8693(80)90194-5},
       URL = {http://dx.doi.org/10.1016/0021-8693(80)90194-5},
}

@book {Hartshorne,
    AUTHOR = {Hartshorne, Robin},
     TITLE = {Algebraic geometry},
      NOTE = {Graduate Texts in Mathematics, No. 52},
 PUBLISHER = {Springer-Verlag, New York-Heidelberg},
      YEAR = {1977},
     PAGES = {xvi+496},
      ISBN = {0-387-90244-9},
   MRCLASS = {14-01},
  MRNUMBER = {0463157},
MRREVIEWER = {Robert Speiser},
}

@book {Hazewinkel,
    AUTHOR = {Hazewinkel, Michiel},
     TITLE = {Formal groups and applications},
      NOTE = {Corrected reprint of the 1978 original},
 PUBLISHER = {AMS Chelsea Publishing, Providence, RI},
      YEAR = {2012},
     PAGES = {xxvi+573},
      ISBN = {978-0-8218-5349-8},
   MRCLASS = {14L05 (11F85 13F35)},
  MRNUMBER = {2987372},
}

@article {HedayatzadehFieldCase,
    AUTHOR = {Hedayatzadeh, S. Mohammad Hadi},
     TITLE = {Exterior powers of {$\pi$}-divisible modules over fields},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {138},
      YEAR = {2014},
     PAGES = {119--174},
      ISSN = {0022-314X},
   MRCLASS = {11S85},
  MRNUMBER = {3168925},
       DOI = {10.1016/j.jnt.2013.10.023},
       URL = {http://dx.doi.org/10.1016/j.jnt.2013.10.023},
}

% this could be updated
@ARTICLE{HedayatzadehGeneralCase,
    AUTHOR = {Hedayatzadeh, S. Mohammad Hadi},
     TITLE = {Exterior powers of {L}ubin-{T}ate groups},
   JOURNAL = {J. Th\'eor. Nombres Bordeaux},
  FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux},
    VOLUME = {27},
      YEAR = {2015},
    NUMBER = {1},
     PAGES = {77--148},
      ISSN = {1246-7405},
   MRCLASS = {14L05},
  MRNUMBER = {3346966},
MRREVIEWER = {Noriko Yui},
       URL = {http://jtnb.cedram.org/item?id=JTNB_2015__27_1_77_0},
}

@ARTICLE{Heuts,
   author = {{Heuts}, Gijs},
    title = "{Lie algebras and $v_n$-periodic spaces}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1803.06325},
 primaryClass = "math.AT",
     year = 2018,
    month = mar,
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@book {Hida,
    AUTHOR = {Hida, Haruzo},
     TITLE = {{$p$}-adic automorphic forms on {S}himura varieties},
    SERIES = {Springer Monographs in Mathematics},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {2004},
     PAGES = {xii+390},
      ISBN = {0-387-20711-2},
   MRCLASS = {11F33 (11F46 11F85 11G18)},
  MRNUMBER = {2055355},
MRREVIEWER = {Jacques Tilouine},
       DOI = {10.1007/978-1-4684-9390-0},
       URL = {http://dx.doi.org/10.1007/978-1-4684-9390-0},
}

@ARTICLE{HillHopkins,
   author = {{Hill}, M.~A. and {Hopkins}, M.~J.},
    title = "{Real Wilson Spaces I}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1806.11033},
 primaryClass = "math.AT",
 keywords = {Mathematics - Algebraic Topology, 55N91},
     year = 2018,
    month = jun,
   adsurl = {http://adsabs.harvard.edu/abs/2018arXiv180611033H},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{HHR,
  title={On the nonexistence of elements of {K}ervaire invariant one},
  author={Hill, Michael A and Hopkins, Michael J and Ravenel, Douglas C},
  journal={Annals of Mathematics},
  volume={184},
  number={1},
  pages={1--262},
  year={2016},
  publisher={Princeton University and the Institute for Advanced Study}
}

@book {Hirzebruch,
    AUTHOR = {Hirzebruch, Friedrich},
     TITLE = {Topological methods in algebraic geometry},
    SERIES = {Classics in Mathematics},
      NOTE = {Translated from the German and Appendix One by R. L. E.
              Schwarzenberger,
              With a preface to the third English edition by the author and
              Schwarzenberger,
              Appendix Two by A. Borel,
              Reprint of the 1978 edition},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {1995},
     PAGES = {xii+234},
      ISBN = {3-540-58663-6},
   MRCLASS = {57-02 (01A75 14-02)},
  MRNUMBER = {1335917},
}

@ARTICLE{HopkinsCOCTALOS,
  author = {Hopkins, Michael J.},
  title = {Complex oriented cohomology theories and the language of stacks},
  journal = {Unpublished},
  URL = {https://www.math.rochester.edu/people/faculty/doug/otherpapers/coctalos.pdf}
}

@incollection {HopkinsFromSpectraToStacks,
    AUTHOR = {Hopkins, Michael J.},
     TITLE = {From Spectra to Stacks},
 BOOKTITLE = {Topological Modular Forms},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {201},
     PAGES = {118--126},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2014},
}

@article{HAS,
  author = {Hopkins, Michael and Ando, Matthew and Strickland, Neil},
  title = {Elliptic Cohomology of {$BO\<8\>$} in Positive Charactersitic},
  year = {1999},
  note = {Unpublished preprint}
}

@article {HopkinsGrossAnnouncement,
    AUTHOR = {Hopkins, M. J. and Gross, B. H.},
     TITLE = {The rigid analytic period mapping, {L}ubin-{T}ate space, and
              stable homotopy theory},
   JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
  FJOURNAL = {American Mathematical Society. Bulletin. New Series},
    VOLUME = {30},
      YEAR = {1994},
    NUMBER = {1},
     PAGES = {76--86},
      ISSN = {0273-0979},
     CODEN = {BAMOAD},
   MRCLASS = {55N22 (11S31 14F30 14L05 55P42)},
  MRNUMBER = {1217353},
MRREVIEWER = {N. J. Kuhn},
       DOI = {10.1090/S0273-0979-1994-00438-0},
       URL = {http://dx.doi.org/10.1090/S0273-0979-1994-00438-0},
}

@incollection {HopkinsGrossEquivVBs,
    AUTHOR = {Hopkins, M. J. and Gross, B. H.},
     TITLE = {Equivariant vector bundles on the {L}ubin-{T}ate moduli space},
 BOOKTITLE = {Topology and representation theory ({E}vanston, {IL}, 1992)},
    SERIES = {Contemp. Math.},
    VOLUME = {158},
     PAGES = {23--88},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1994},
   MRCLASS = {14L05 (11S31 12H25 55R91)},
  MRNUMBER = {1263712},
MRREVIEWER = {Burt Totaro},
       DOI = {10.1090/conm/158/01453},
       URL = {http://dx.doi.org/10.1090/conm/158/01453},
}

@inproceedings {HopkinsICMBeijing,
    AUTHOR = {Hopkins, M. J.},
     TITLE = {Algebraic topology and modular forms},
 BOOKTITLE = {Proceedings of the {I}nternational {C}ongress of
              {M}athematicians, {V}ol. {I} ({B}eijing, 2002)},
     PAGES = {291--317},
 PUBLISHER = {Higher Ed. Press, Beijing},
      YEAR = {2002},
   MRCLASS = {11F23 (14H52 55N34 55Q45)},
  MRNUMBER = {1989190},
MRREVIEWER = {Matthew Ando},
}

@inproceedings {HopkinsICMZurich,
    AUTHOR = {Hopkins, Michael J.},
     TITLE = {Topological modular forms, the {W}itten genus, and the theorem
              of the cube},
 BOOKTITLE = {Proceedings of the {I}nternational {C}ongress of
              {M}athematicians, {V}ol.\ 1, 2 ({Z}\"urich, 1994)},
     PAGES = {554--565},
 PUBLISHER = {Birkh\"auser, Basel},
      YEAR = {1995},
   MRCLASS = {11F11 (55N22 55P42 57R77 58G12)},
  MRNUMBER = {1403956},
MRREVIEWER = {Andrew J. Baker},
}

@incollection {HopkinsK1LocalEinftyRings,
    AUTHOR = {Hopkins, Michael J.},
     TITLE = {{$K(1)$}-local {$E_\infty$} ring spectra},
 BOOKTITLE = {Topological Modular Forms},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {201},
     PAGES = {301--216},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2014},
}

@article {HopkinsOnRavenel,
    AUTHOR = {Hopkins, Michael J.},
     TITLE = {The mathematical work of {D}ouglas {C}. {R}avenel},
   JOURNAL = {Homology Homotopy Appl.},
  FJOURNAL = {Homology, Homotopy and Applications},
    VOLUME = {10},
      YEAR = {2008},
    NUMBER = {3},
     PAGES = {1--13},
      ISSN = {1532-0073},
   MRCLASS = {55-02 (55N22 55Q51 55T15)},
  MRNUMBER = {2475614},
MRREVIEWER = {Haynes R. Miller},
       URL = {http://projecteuclid.org/euclid.hha/1201127511},
}

@incollection {HopkinsTheStringOrientation,
    AUTHOR = {Hopkins, Michael J.},
     TITLE = {The String Orientation},
 BOOKTITLE = {Topological Modular Forms},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {201},
     PAGES = {127--142},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2014},
}

@article{HopkinsHovey,
  title={Spin cobordism determines real {$K$}-theory},
  author={Hopkins, Michael J and Hovey, Mark A},
  journal={Mathematische Zeitschrift},
  volume={210},
  number={1},
  pages={181--196},
  year={1992},
  publisher={Springer}
}

@article {HopkinsHunton,
    AUTHOR = {Hopkins, M. J. and Hunton, J. R.},
     TITLE = {On the structure of spaces representing a {L}andweber exact
              cohomology theory},
   JOURNAL = {Topology},
  FJOURNAL = {Topology. An International Journal of Mathematics},
    VOLUME = {34},
      YEAR = {1995},
    NUMBER = {1},
     PAGES = {29--36},
      ISSN = {0040-9383},
     CODEN = {TPLGAF},
   MRCLASS = {55N20 (55N22)},
  MRNUMBER = {1308488},
MRREVIEWER = {Andrew J. Baker},
       DOI = {10.1016/0040-9383(94)E0013-A},
       URL = {http://dx.doi.org/10.1016/0040-9383(94)E0013-A},
}

@article {HKR,
    AUTHOR = {Hopkins, Michael J. and Kuhn, Nicholas J. and Ravenel, Douglas
              C.},
     TITLE = {Generalized group characters and complex oriented cohomology
              theories},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {13},
      YEAR = {2000},
    NUMBER = {3},
     PAGES = {553--594 (electronic)},
      ISSN = {0894-0347},
   MRCLASS = {55N22 (55N20 55N91 55R40)},
  MRNUMBER = {1758754 (2001k:55015)},
MRREVIEWER = {Andrew J. Baker},
       DOI = {10.1090/S0894-0347-00-00332-5},
       URL = {http://dx.doi.org/10.1090/S0894-0347-00-00332-5},
}

@article{HopkinsLawson,
  title={Strictly commutative complex orientation theory},
  author={Hopkins, Michael J and Lawson, Tyler},
  journal={arXiv preprint arXiv:1603.00047},
  year={2016}
}

@ARTICLE{HopkinsLurie,
  author = {Hopkins, Michael J. and Lurie, Jacob},
  title = {Ambidexterity in {$K(n)$}-local stable homotopy theory},
  note = {\url{http://www.math.harvard.edu/~lurie/papers/Ambidexterity.pdf}, Accessed: 2015-01-09}
}

@incollection {HMS,
    AUTHOR = {Hopkins, Michael J. and Mahowald, Mark and Sadofsky, Hal},
     TITLE = {Constructions of elements in {P}icard groups},
 BOOKTITLE = {Topology and representation theory ({E}vanston, {IL}, 1992)},
    SERIES = {Contemp. Math.},
    VOLUME = {158},
     PAGES = {89--126},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1994},
   MRCLASS = {55P42 (55P60 55Q10)},
  MRNUMBER = {1263713 (95a:55020)},
MRREVIEWER = {Dominique Arlettaz},
}

@incollection {HopkinsMiller,
    AUTHOR = {Hopkins, Michael J. and Miller, Haynes R.},
     TITLE = {Elliptic Curves and Stable Homotopy Theory {I}},
 BOOKTITLE = {Topological Modular Forms},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {201},
     PAGES = {224-275},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2014},
}

@article {HopkinsSmith,
    AUTHOR = {Hopkins, Michael J. and Smith, Jeffrey H.},
     TITLE = {Nilpotence and stable homotopy theory. {II}},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {148},
      YEAR = {1998},
    NUMBER = {1},
     PAGES = {1--49},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {55P42 (55N20 55Q10)},
  MRNUMBER = {1652975 (99h:55009)},
MRREVIEWER = {David A. Blanc},
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}

@incollection {HoveyCSC,
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}

@incollection {HoveyHomotopyOfComodules,
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     TITLE = {Homotopy theory of comodules over a {H}opf algebroid},
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@article {HoveyMoritaThy,
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MRREVIEWER = {Gabriele Vezzosi},
       URL =
              {http://muse.jhu.edu/journals/american_journal_of_mathematics/v124/124.6hovey.pdf},
}

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       URL = {https://doi.org/10.1090/S0894-0347-99-00320-3},
}

@article {HoveyStrickland,
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MRREVIEWER = {J. P. C. Greenlees},
}

@article{Huan,
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@book {Husemoller,
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@article{JohnsonNoel,
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    SERIES = {Tata Inst. Fund. Res. Studies in Math.},
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      YEAR = {1981},
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@incollection {KatzSTLocalModuli,
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    SERIES = {Lecture Notes in Math.},
    VOLUME = {868},
     PAGES = {80--137},
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      YEAR = {1981},
   MRCLASS = {14F30 (14J25)},
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MRREVIEWER = {William E. Lang},
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@book {KatzMazur,
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MRREVIEWER = {Kenneth A. Ribet},
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@inproceedings{Kitaev,
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    NUMBER = {3},
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@phdthesis{KnightThesis,
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@article {LandweberHomologicalComodules,
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@article {LandweberInvariantRegIdeals,
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@article{LRS,
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@article {LauresK1LocalTmf,
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@article {LauresSplitting,
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@ARTICLE{LauresSchuster,
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  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1710.03427},
 primaryClass = "math.AT",
 keywords = {Mathematics - Algebraic Topology},
     year = 2017,
    month = oct,
   adsurl = {http://adsabs.harvard.edu/abs/2017arXiv171003427L},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

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@article {LawsonRealizability,
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@article{LawsonSecondaryPowerOps,
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   MRCLASS = {55N22 (14L05)},
  MRNUMBER = {1452853},
MRREVIEWER = {Keith Peter Johnson},
       DOI = {10.1016/S0040-9383(96)00051-1},
       URL = {http://dx.doi.org/10.1016/S0040-9383(96)00051-1},
}

@incollection {LazarevStructured,
    AUTHOR = {Lazarev, A.},
     TITLE = {Spaces of multiplicative maps between highly structured ring
              spectra},
 BOOKTITLE = {Categorical decomposition techniques in algebraic topology
              ({I}sle of {S}kye, 2001)},
    SERIES = {Progr. Math.},
    VOLUME = {215},
     PAGES = {237--259},
 PUBLISHER = {Birkh\"auser, Basel},
      YEAR = {2004},
   MRCLASS = {55P43},
  MRNUMBER = {2039769 (2005g:55010)},
MRREVIEWER = {Birgit Richter},
}

@book {LMS,
    AUTHOR = {Lewis, Jr., L. G. and May, J. P. and Steinberger, M. and
              McClure, J. E.},
     TITLE = {Equivariant stable homotopy theory},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {1213},
      NOTE = {With contributions by J. E. McClure},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {1986},
     PAGES = {x+538},
      ISBN = {3-540-16820-6},
   MRCLASS = {55-02 (55Nxx 55Pxx 57S99)},
  MRNUMBER = {866482},
MRREVIEWER = {T. tom Dieck},
       DOI = {10.1007/BFb0075778},
       URL = {https://doi.org/10.1007/BFb0075778},
}

@article {Lin,
    AUTHOR = {Lin, Wen Hsiung},
     TITLE = {On conjectures of {M}ahowald, {S}egal and {S}ullivan},
   JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
  FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
              Society},
    VOLUME = {87},
      YEAR = {1980},
    NUMBER = {3},
     PAGES = {449--458},
      ISSN = {0305-0041},
     CODEN = {MPCPCO},
   MRCLASS = {55Q10},
  MRNUMBER = {556925 (81e:55020)},
MRREVIEWER = {Donald M. Davis},
       DOI = {10.1017/S0305004100056887},
       URL = {http://dx.doi.org/10.1017/S0305004100056887},
}

@article{Lubin,
 ISSN = {0003486X},
 URL = {http://www.jstor.org/stable/1970443},
 author = {Jonathan Lubin},
 journal = {Annals of Mathematics},
 number = {2},
 pages = {296-302},
 publisher = {Annals of Mathematics},
 title = {Finite Subgroups and Isogenies of One-Parameter Formal Lie Groups},
 volume = {85},
 year = {1967}
}

@article {LubinTate,
    AUTHOR = {Lubin, Jonathan and Tate, John},
     TITLE = {Formal moduli for one-parameter formal {L}ie groups},
   JOURNAL = {Bull. Soc. Math. France},
  FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique de France},
    VOLUME = {94},
      YEAR = {1966},
     PAGES = {49--59},
      ISSN = {0037-9484},
   MRCLASS = {14.50},
  MRNUMBER = {0238854 (39 \#214)},
MRREVIEWER = {J. Dieudonn{\'e}},
}

@article{LubinTateOther,
  title={Formal complex multiplication in local fields},
  author={Lubin, Jonathan and Tate, John},
  journal={Annals of Mathematics},
  pages={380--387},
  year={1965},
  publisher={JSTOR}
}

@BOOK{LurieChromaticCourseNotes,
  author = {Lurie, Jacob},
  title = {Chromatic Homotopy},
  note = {\url{http://www.math.harvard.edu/~lurie/252x.html}, Accessed: 2016-09-22}
}

@BOOK{LurieEllII,
  author = {Lurie, Jacob},
  title = {Elliptic Cohomology {II}: {O}rientations},
  note = {\url{http://math.harvard.edu/~lurie/papers/Elliptic-II.pdf}, Accessed: 2018-02-04}
}

@BOOK{LurieHA,
  author = {Lurie, Jacob},
  title = {Higher Algebra},
  note = {\url{http://www.math.harvard.edu/~lurie/papers/HA.pdf}, Accessed: 2016-09-22}
}

@book {LurieHTT,
    AUTHOR = {Lurie, Jacob},
     TITLE = {Higher topos theory},
    SERIES = {Annals of Mathematics Studies},
    VOLUME = {170},
 PUBLISHER = {Princeton University Press, Princeton, NJ},
      YEAR = {2009},
     PAGES = {xviii+925},
      ISBN = {978-0-691-14049-0; 0-691-14049-9},
   MRCLASS = {18-02 (18B25 18E35 18G30 18G55 55U40)},
  MRNUMBER = {2522659},
MRREVIEWER = {Mark Hovey},
       DOI = {10.1515/9781400830558},
       URL = {http://dx.doi.org/10.1515/9781400830558},
}

@BOOK{LurieSAG,
  author = {Lurie, Jacob},
  title = {Spectral Algebraic Geometry},
  note = {\url{http://www.math.harvard.edu/~lurie/papers/SAG-rootfile.pdf}, Accessed: 2016-09-22}
}

@ARTICLE{LurieSurveyOfEll,
  author = {Lurie, Jacob},
  title = {A Survey of Elliptic Cohomology},
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}

@article {Mahowald,
    AUTHOR = {Mahowald, Mark},
     TITLE = {Ring spectra which are {T}hom complexes},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {46},
      YEAR = {1979},
    NUMBER = {3},
     PAGES = {549--559},
      ISSN = {0012-7094},
   MRCLASS = {55P99 (55N20)},
  MRNUMBER = {544245},
MRREVIEWER = {Edgar H. Brown, Jr.},
       URL = {http://projecteuclid.org/euclid.dmj/1077313574},
}

@article{MahowaldRavenel,
  title={The root invariant in homotopy theory},
  author={Mahowald, Mark E and Ravenel, Douglas C},
  journal={Topology},
  volume={32},
  number={4},
  pages={865--898},
  year={1993},
  publisher={Elsevier}
}

@incollection {MRS,
    AUTHOR = {Mahowald, Mark and Ravenel, Douglas and Shick, Paul},
     TITLE = {The triple loop space approach to the telescope conjecture},
 BOOKTITLE = {Homotopy methods in algebraic topology ({B}oulder, {CO},
              1999)},
    SERIES = {Contemp. Math.},
    VOLUME = {271},
     PAGES = {217--284},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2001},
   MRCLASS = {55P42 (55P35 55P60 55T10)},
  MRNUMBER = {1831355},
MRREVIEWER = {N. J. Kuhn},
       URL = {https://doi.org/10.1090/conm/271/04358},
}

@article {MahowaldSadofsky,
    AUTHOR = {Mahowald, Mark and Sadofsky, Hal},
     TITLE = {{$v_n$} telescopes and the {A}dams spectral sequence},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {78},
      YEAR = {1995},
    NUMBER = {1},
     PAGES = {101--129},
      ISSN = {0012-7094},
   MRCLASS = {55P42 (55P60 55Q10 55T15)},
  MRNUMBER = {1328754},
MRREVIEWER = {N. J. Kuhn},
       URL = {https://doi.org/10.1215/S0012-7094-95-07806-5},
}

@article{MahowaldShick,
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  author={Mahowald, Mark and Shick, Paul},
  journal={Bulletin of the London Mathematical Society},
  volume={20},
  number={3},
  pages={262--266},
  year={1988},
  publisher={Wiley Online Library}
}

@article {MahowaldThompson,
    AUTHOR = {Mahowald, Mark and Thompson, Robert D.},
     TITLE = {The {$K$}-theory localization of an unstable sphere},
   JOURNAL = {Topology},
  FJOURNAL = {Topology. An International Journal of Mathematics},
    VOLUME = {31},
      YEAR = {1992},
    NUMBER = {1},
     PAGES = {133--141},
      ISSN = {0040-9383},
   MRCLASS = {55P60 (55N15)},
  MRNUMBER = {1153241},
MRREVIEWER = {Donald M. Davis},
       DOI = {10.1016/0040-9383(92)90066-Q},
       URL = {http://dx.doi.org/10.1016/0040-9383(92)90066-Q},
}

@article {Mandell,
    AUTHOR = {Mandell, Michael A.},
     TITLE = {{$E_\infty$} algebras and {$p$}-adic homotopy theory},
   JOURNAL = {Topology},
  FJOURNAL = {Topology. An International Journal of Mathematics},
    VOLUME = {40},
      YEAR = {2001},
    NUMBER = {1},
     PAGES = {43--94},
      ISSN = {0040-9383},
   MRCLASS = {55P15 (55P60)},
  MRNUMBER = {1791268},
MRREVIEWER = {Paul G. Goerss},
       DOI = {10.1016/S0040-9383(99)00053-1},
       URL = {https://doi.org/10.1016/S0040-9383(99)00053-1},
}

@article{Manin,
  title={The theory of commutative formal groups over fields of finite characteristic},
  author={Manin, Yu I},
  journal={Russian Mathematical Surveys},
  volume={18},
  number={6},
  pages={1},
  year={1963},
  publisher={IOP Publishing}
}

@book {Margolis,
    AUTHOR = {Margolis, H. R.},
     TITLE = {Spectra and the {S}teenrod algebra},
    SERIES = {North-Holland Mathematical Library},
    VOLUME = {29},
      NOTE = {Modules over the Steenrod algebra and the stable homotopy
              category},
 PUBLISHER = {North-Holland Publishing Co., Amsterdam},
      YEAR = {1983},
     PAGES = {xix+489},
      ISBN = {0-444-86516-0},
   MRCLASS = {55-02 (55Sxx)},
  MRNUMBER = {738973},
MRREVIEWER = {Andrzej Kozlowski},
}

@article{MathewMeier,
  title={Affineness and chromatic homotopy theory},
  author={Mathew, Akhil and Meier, Lennart},
  journal={Journal of Topology},
  volume={8},
  number={2},
  pages={476--528},
  year={2015},
  publisher={Oxford University Press}
}

@article{Mathew,
title = "The Galois group of a stable homotopy theory",
journal = "Advances in Mathematics",
volume = "291",
pages = "403 - 541",
year = "2016",
issn = "0001-8708",
doi = "https://doi.org/10.1016/j.aim.2015.12.017",
url = "http://www.sciencedirect.com/science/article/pii/S000187081500554X",
author = "Akhil Mathew",
}

@article {MNNDescent,
    AUTHOR = {Mathew, Akhil and Naumann, Niko and Noel, Justin},
     TITLE = {Nilpotence and descent in equivariant stable homotopy theory},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {305},
      YEAR = {2017},
     PAGES = {994--1084},
      ISSN = {0001-8708},
   MRCLASS = {55P91 (55P42)},
  MRNUMBER = {3570153},
MRREVIEWER = {Gregory Z. Arone},
       DOI = {10.1016/j.aim.2016.09.027},
       URL = {https://doi.org/10.1016/j.aim.2016.09.027},
}

@article{MNNNilpotence,
author = {Mathew, Akhil and Naumann, Niko and Noel, Justin},
title = {On a nilpotence conjecture of J. P. May},
journal = {Journal of Topology},
volume = {8},
number = {4},
pages = {917-932},
year = {2015},
doi = {10.1112/jtopol/jtv021},
URL = {http://dx.doi.org/10.1112/jtopol/jtv021},
eprint = {/oup/backfile/content_public/journal/jtopol/8/4/10.1112/jtopol/jtv021/2/jtv021.pdf}
}

@book {Matsumura,
    AUTHOR = {Matsumura, Hideyuki},
     TITLE = {Commutative ring theory},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {8},
   EDITION = {Second},
      NOTE = {Translated from the Japanese by M. Reid},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1989},
     PAGES = {xiv+320},
      ISBN = {0-521-36764-6},
   MRCLASS = {13-01},
  MRNUMBER = {1011461 (90i:13001)},
}

@book {MayAlaskaNotes,
    AUTHOR = {May, J. P.},
     TITLE = {Equivariant homotopy and cohomology theory},
    SERIES = {CBMS Regional Conference Series in Mathematics},
    VOLUME = {91},
      NOTE = {With contributions by M. Cole, G. Comeza\~na, S. Costenoble, A.
              D. Elmendorf, J. P. C. Greenlees, L. G. Lewis, Jr., R. J.
              Piacenza, G. Triantafillou, and S. Waner},
 PUBLISHER = {Published for the Conference Board of the Mathematical
              Sciences, Washington, DC; by the American Mathematical
              Society, Providence, RI},
      YEAR = {1996},
     PAGES = {xiv+366},
      ISBN = {0-8218-0319-0},
   MRCLASS = {55P91 (18G99 55N91 55U35)},
  MRNUMBER = {1413302},
MRREVIEWER = {Ian Hambleton},
       DOI = {10.1090/cbms/091},
       URL = {http://dx.doi.org/10.1090/cbms/091},
}

@article {MayClassifyingSpaces,
    AUTHOR = {May, J. Peter},
     TITLE = {Classifying spaces and fibrations},
   JOURNAL = {Mem. Amer. Math. Soc.},
  FJOURNAL = {Memoirs of the American Mathematical Society},
    VOLUME = {1},
      YEAR = {1975},
    NUMBER = {1, 155},
     PAGES = {xiii+98},
      ISSN = {0065-9266},
   MRCLASS = {55F15 (57F20)},
  MRNUMBER = {0370579},
MRREVIEWER = {Harold Hastings},
}


@book {MayConciseCourse,
    AUTHOR = {May, J. P.},
     TITLE = {A concise course in algebraic topology},
    SERIES = {Chicago Lectures in Mathematics},
 PUBLISHER = {University of Chicago Press, Chicago, IL},
      YEAR = {1999},
     PAGES = {x+243},
      ISBN = {0-226-51182-0; 0-226-51183-9},
   MRCLASS = {55-02 (18-02 57-02)},
  MRNUMBER = {1702278},
MRREVIEWER = {R. M. Vogt},
}

@inproceedings{MayProblemsInLoopspaceTheory,
  title={Problems in infinite loop space theory},
  author={May, JP},
  booktitle={Notas de Matemfiticas y Simposio, Ntimero},
  volume={1},
  pages={111--125},
  year={1974}
}

@book {MayRingSpacesSpectra,
    AUTHOR = {May, J. Peter},
     TITLE = {{$E_{\infty }$} ring spaces and {$E_{\infty }$} ring
              spectra},
    SERIES = {Lecture Notes in Mathematics, Vol. 577},
      NOTE = {With contributions by Frank Quinn, Nigel Ray, and J\o rgen
              Tornehave},
 PUBLISHER = {Springer-Verlag, Berlin-New York},
      YEAR = {1977},
     PAGES = {268},
   MRCLASS = {55D35},
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MRREVIEWER = {J. Stasheff},
}

@Article{Mazur,
author="Mazur, B. and Swinnerton-Dyer, P.",
title="Arithmetic of Weil curves",
journal="Inventiones mathematicae",
year="1974",
month="Mar",
day="01",
volume="25",
number="1",
pages="1--61",
issn="1432-1297",
doi="10.1007/BF01389997",
url="https://doi.org/10.1007/BF01389997"
}

@book {MazurMessing,
    AUTHOR = {Mazur, B. and Messing, William},
     TITLE = {Universal extensions and one dimensional crystalline
              cohomology},
    SERIES = {Lecture Notes in Mathematics, Vol. 370},
 PUBLISHER = {Springer-Verlag, Berlin-New York},
      YEAR = {1974},
     PAGES = {vii+134},
   MRCLASS = {14K05 (14F30 14G05 14L05)},
  MRNUMBER = {0374150},
MRREVIEWER = {S. Bloch},
}

@article {McClure,
    AUTHOR = {McClure, James E.},
     TITLE = {Dyer-{L}ashof operations in {$K$}-theory},
   JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
  FJOURNAL = {American Mathematical Society. Bulletin. New Series},
    VOLUME = {8},
      YEAR = {1983},
    NUMBER = {1},
     PAGES = {67--72},
      ISSN = {0273-0979},
   MRCLASS = {55S12 (55P47)},
  MRNUMBER = {682824},
MRREVIEWER = {Harvey Margolis},
       URL = {https://doi.org/10.1090/S0273-0979-1983-15086-3},
}

@article{McTague,
  title={{$\tmf$} is not a ring spectrum quotient of {$\String$} bordism},
  author={McTague, Carl},
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  year={2013}
}

@book {Messing,
    AUTHOR = {Messing, William},
     TITLE = {The crystals associated to {B}arsotti-{T}ate groups: with
              applications to abelian schemes},
    SERIES = {Lecture Notes in Mathematics, Vol. 264},
 PUBLISHER = {Springer-Verlag, Berlin-New York},
      YEAR = {1972},
     PAGES = {iii+190},
   MRCLASS = {14L05 (14B20 14D15 14F30 14K10)},
  MRNUMBER = {0347836},
MRREVIEWER = {F. Oort},
}

@incollection {Michaelis,
    AUTHOR = {Michaelis, Walter},
     TITLE = {Coassociative coalgebras},
 BOOKTITLE = {Handbook of algebra, {V}ol. 3},
     PAGES = {587--788},
 PUBLISHER = {North-Holland, Amsterdam},
      YEAR = {2003},
   MRCLASS = {16W30 (00A20)},
  MRNUMBER = {2035107 (2005b:16070)},
MRREVIEWER = {E. J. Taft},
       DOI = {10.1016/S1570-7954(03)80072-4},
       URL = {http://dx.doi.org/10.1016/S1570-7954(03)80072-4},
}

@incollection {MillerBernoulliNos,
    AUTHOR = {Miller, Haynes},
     TITLE = {Universal {B}ernoulli numbers and the {$S^{1}$}-transfer},
 BOOKTITLE = {Current trends in algebraic topology, {P}art 2 ({L}ondon,
              {O}nt., 1981)},
    SERIES = {CMS Conf. Proc.},
    VOLUME = {2},
     PAGES = {437--449},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1982},
   MRCLASS = {55R99},
  MRNUMBER = {686158},
MRREVIEWER = {Mark Feshbach},
}

@BOOK{MillerNotesCobordism,
  author = {Miller, Haynes},
  title = {Notes on Cobordism},
  note = {\url{www-math.mit.edu/~hrm/papers/cobordism.pdf}, Accessed: 2016-10-04}
}

@article{MillerRelations,
title = "On relations between Adams spectral sequences, with an application to the stable homotopy of a moore space",
journal = "Journal of Pure and Applied Algebra",
volume = "20",
number = "3",
pages = "287 - 312",
year = "1981",
issn = "0022-4049",
doi = "https://doi.org/10.1016/0022-4049(81)90064-5",
url = "http://www.sciencedirect.com/science/article/pii/0022404981900645",
author = "Haynes R. Miller"
}

@ARTICLE{MillerSheavesGradings,
  author = {Miller, Haynes},
  title = {Sheaves, gradings, and the exact functor theorem},
  journal = {Unpublished},
  URL = {http://www-math.mit.edu/~hrm/papers/bcat.pdf}
}

@article {MRW,
    AUTHOR = {Miller, Haynes R. and Ravenel, Douglas C. and Wilson, W.
              Stephen},
     TITLE = {Periodic phenomena in the {A}dams-{N}ovikov spectral sequence},
   JOURNAL = {Ann. of Math. (2)},
    VOLUME = {106},
      YEAR = {1977},
    NUMBER = {3},
     PAGES = {469--516},
   MRCLASS = {55E45 (55H15)},
  MRNUMBER = {0458423},
MRREVIEWER = {J. F. Adams},
}

@book {Milne,
    AUTHOR = {Milne, J. S.},
     TITLE = {Abelian varieties},
      NOTE = {\url{http://www.jmilne.org/math/CourseNotes/av.html}},
      YEAR = {2008},
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@article{milneabelian,
  title={Abelian varieties (v2. 00), 2008},
  author={Milne, James S},
  
}

@article {Milnor,
    AUTHOR = {Milnor, John},
     TITLE = {The {S}teenrod algebra and its dual},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {67},
      YEAR = {1958},
     PAGES = {150--171},
      ISSN = {0003-486X},
   MRCLASS = {55.00 (18.00)},
  MRNUMBER = {0099653 (20 \#6092)},
MRREVIEWER = {G. Hirsch},
}

@article {MilnorMoore,
    AUTHOR = {Milnor, John W. and Moore, John C.},
     TITLE = {On the structure of {H}opf algebras},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {81},
      YEAR = {1965},
     PAGES = {211--264},
      ISSN = {0003-486X},
   MRCLASS = {55.40 (55.34)},
  MRNUMBER = {0174052},
MRREVIEWER = {I. M. James},
}

@inproceedings {Mitchell,
    AUTHOR = {Mitchell, Stephen A.},
     TITLE = {Power series methods in unoriented cobordism},
 BOOKTITLE = {Proceedings of the {N}orthwestern {H}omotopy {T}heory
              {C}onference ({E}vanston, {I}ll., 1982)},
    SERIES = {Contemp. Math.},
    VOLUME = {19},
     PAGES = {247--254},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1983},
   MRCLASS = {57R75 (55N22 57R77)},
  MRNUMBER = {711056},
MRREVIEWER = {Edgar H. Brown, Jr.},
       DOI = {10.1090/conm/019/711056},
       URL = {http://dx.doi.org/10.1090/conm/019/711056},
}

@incollection{MitchellIwasawa,
  title={{$K(1)$}-local homotopy theory, Iwasawa theory, and algebraic {$K$}-theory},
  author={Mitchell, Stephen A},
  year={2005},
  booktitle={Handbook of K-theory},
  publisher={Springer Science \& Business Media}
}

@article{MoravaAbVarsAndKervaire,
  title={Abelian varieties and the {K}ervaire invariant},
  author={Morava, Jack},
  journal={arXiv preprint arXiv:1105.0539},
  year={2011}
}

@article {MoravaFormsOfKthy,
    AUTHOR = {Morava, Jack},
     TITLE = {Forms of {$K$}-theory},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {201},
      YEAR = {1989},
    NUMBER = {3},
     PAGES = {401--428},
      ISSN = {0025-5874},
     CODEN = {MAZEAX},
   MRCLASS = {55N22 (11S31)},
  MRNUMBER = {999737},
MRREVIEWER = {P. S. Landweber},
       DOI = {10.1007/BF01214905},
       URL = {http://dx.doi.org/10.1007/BF01214905},
}

@article{MoravaLocalFieldsExtraordinaryKthy,
  title={Local fields and extraordinary {$K$}-theory},
  author={Morava, Jack},
  journal={arXiv preprint arXiv:1207.4011},
  year={2012}
}

@article {MoravaCobordismComodules,
    AUTHOR = {Morava, Jack},
     TITLE = {Noetherian localisations of categories of cobordism comodules},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {121},
      YEAR = {1985},
    NUMBER = {1},
     PAGES = {1--39},
      ISSN = {0003-486X},
   MRCLASS = {55N22 (14L05 14L15 57R77)},
  MRNUMBER = {782555 (86g:55004)},
MRREVIEWER = {Douglas C. Ravenel},
       DOI = {10.2307/1971192},
       URL = {http://dx.doi.org/10.2307/1971192},
}

@article{MoravaCplxBordismInAT,
  author = {Morava, Jack},
  title = {Complex cobordism in algebraic topology},
  archivePrefix = "arXiv",
  eprint = {0707.3216},
  primaryClass = "math.AT",
  year = {2007}
}

@incollection {MoravaMotivicThomIso,
    AUTHOR = {Morava, Jack},
     TITLE = {The motivic {T}hom isomorphism},
 BOOKTITLE = {Elliptic cohomology},
    SERIES = {London Math. Soc. Lecture Note Ser.},
    VOLUME = {342},
     PAGES = {265--285},
 PUBLISHER = {Cambridge Univ. Press, Cambridge},
      YEAR = {2007},
   MRCLASS = {55N22 (11G09 14F42 57R77)},
  MRNUMBER = {2330517},
MRREVIEWER = {Mark Hovey},
       DOI = {10.1017/CBO9780511721489.014},
       URL = {http://dx.doi.org/10.1017/CBO9780511721489.014},
}

@article{MoravaTHH,
  author = {Morava, Jack},
  title = {Complex orientations for {$THH$} of some perfectoid fields},
  archivePrefix = "arXiv",
  eprint = {1608.04702},
  primaryClass = "math.AT",
  year = {2016}
}

@article {Morton,
    AUTHOR = {Morton, Dena S. Cowen},
     TITLE = {The {H}opf ring for {$b{\rm o}$} and its connective covers},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {210},
      YEAR = {2007},
    NUMBER = {1},
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      ISSN = {0022-4049},
     CODEN = {JPAAA2},
   MRCLASS = {55P43 (55N15)},
  MRNUMBER = {2311183},
MRREVIEWER = {Jes{\'u}s Gonz{\'a}lez},
       DOI = {10.1016/j.jpaa.2006.09.014},
       URL = {http://dx.doi.org/10.1016/j.jpaa.2006.09.014},
}

@article {MortonStrickland,
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     TITLE = {The {H}opf rings for {$K{\rm O}$} and {$K{\rm U}$}},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {166},
      YEAR = {2002},
    NUMBER = {3},
     PAGES = {247--265},
      ISSN = {0022-4049},
     CODEN = {JPAAA2},
   MRCLASS = {55P43 (16W30 55N15)},
  MRNUMBER = {1870619},
MRREVIEWER = {Mark Hovey},
       DOI = {10.1016/S0022-4049(01)00017-2},
       URL = {http://dx.doi.org/10.1016/S0022-4049(01)00017-2},
}

@book {MosherTangora,
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     TITLE = {Cohomology operations and applications in homotopy theory},
 PUBLISHER = {Harper \& Row, Publishers, New York-London},
      YEAR = {1968},
     PAGES = {x+214},
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MRREVIEWER = {Larry Smith},
}

@article {MumfordEquationsI,
    AUTHOR = {Mumford, D.},
     TITLE = {On the equations defining abelian varieties. {I}},
   JOURNAL = {Invent. Math.},
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  MRNUMBER = {0204427},
MRREVIEWER = {J. W. S. Cassels},
       DOI = {10.1007/BF01389737},
       URL = {http://dx.doi.org/10.1007/BF01389737},
}

@article {MumfordEquationsII,
    AUTHOR = {Mumford, D.},
     TITLE = {On the equations defining abelian varieties. {II}},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {3},
      YEAR = {1967},
     PAGES = {75--135},
      ISSN = {0020-9910},
   MRCLASS = {14.51},
  MRNUMBER = {0219541},
MRREVIEWER = {J. W. S. Cassels},
       DOI = {10.1007/BF01389741},
       URL = {http://dx.doi.org/10.1007/BF01389741},
}

@article {MumfordEquationsIII,
    AUTHOR = {Mumford, D.},
     TITLE = {On the equations defining abelian varieties. {III}},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {3},
      YEAR = {1967},
     PAGES = {215--244},
      ISSN = {0020-9910},
   MRCLASS = {14.51},
  MRNUMBER = {0219542},
MRREVIEWER = {J. W. S. Cassels},
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       URL = {http://dx.doi.org/10.1007/BF01425401},
}

@article{Naumann,
  title={The stack of formal groups in stable homotopy theory},
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  year={2007},
  publisher={Elsevier}
}

@article {Nave,
    AUTHOR = {Nave, Lee S.},
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    VOLUME = {171},
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    NUMBER = {1},
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      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {55Q10 (55P42 55Q51)},
  MRNUMBER = {2630045 (2011m:55012)},
MRREVIEWER = {Paul G. Goerss},
       DOI = {10.4007/annals.2010.171.491},
       URL = {http://dx.doi.org/10.4007/annals.2010.171.491},
}

@article {Nishida,
    AUTHOR = {Nishida, Goro},
     TITLE = {The nilpotency of elements of the stable homotopy groups of
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   JOURNAL = {J. Math. Soc. Japan},
  FJOURNAL = {Journal of the Mathematical Society of Japan},
    VOLUME = {25},
      YEAR = {1973},
     PAGES = {707--732},
      ISSN = {0025-5645},
   MRCLASS = {55E45},
  MRNUMBER = {0341485},
MRREVIEWER = {J. F. Adams},
       DOI = {10.2969/jmsj/02540707},
       URL = {http://dx.doi.org/10.2969/jmsj/02540707},
}

@article{OchanineEnrichmentToKO,
  title={Elliptic genera, modular forms over {$KO_*$}, and the Brown-Kervaire invariant},
  author={Ochanine, Serge},
  journal={Mathematische Zeitschrift},
  volume={206},
  number={1},
  pages={277--291},
  year={1991},
  publisher={Springer}
}

@article{OchanineSUModules,
  title={Modules de {$SU$}-bordisme. Applications},
  author={Ochanine, Serge},
  journal={Bull. Soc. Math. Fr},
  volume={115},
  pages={257--289},
  year={1987}
}

@article {Ochanine,
    AUTHOR = {Ochanine, Serge},
     TITLE = {Sur les genres multiplicatifs d\'efinis par des int\'egrales
              elliptiques},
   JOURNAL = {Topology},
  FJOURNAL = {Topology. An International Journal of Mathematics},
    VOLUME = {26},
      YEAR = {1987},
    NUMBER = {2},
     PAGES = {143--151},
      ISSN = {0040-9383},
     CODEN = {TPLGAF},
   MRCLASS = {57R75 (55N22 57R99)},
  MRNUMBER = {895567},
MRREVIEWER = {P. S. Landweber},
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       URL = {http://dx.doi.org/10.1016/0040-9383(87)90055-3},
}

@article{Pengelley,
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  year={1982},
  publisher={JSTOR}
}

@ARTICLE{PetersonStapleton,
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  title = {Isogenies of Formal Groups Laws and Power Operations in the Cohomology Theories {$E_n$}, Revisited},
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}

@book{Polishchuk,
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}

@article{Priddy,
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  year={1980},
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}

@ARTICLE{Pstragowski,
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  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1810.12250},
 primaryClass = "math.AT",
 keywords = {Mathematics - Algebraic Topology},
     year = 2018,
    month = oct,
   adsurl = {http://adsabs.harvard.edu/abs/2018arXiv181012250P},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article {Quillen,
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     TITLE = {Elementary proofs of some results of cobordism theory using
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   JOURNAL = {Advances in Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {7},
      YEAR = {1971},
     PAGES = {29--56 (1971)},
      ISSN = {0001-8708},
   MRCLASS = {57.10},
  MRNUMBER = {0290382 (44 \#7566)},
MRREVIEWER = {T. tom Dieck},
}

@article {QuillenAdamsSS,
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     TITLE = {On the formal group laws of unoriented and complex cobordism
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   JOURNAL = {Bull. Amer. Math. Soc.},
  FJOURNAL = {Bulletin of the American Mathematical Society},
    VOLUME = {75},
      YEAR = {1969},
     PAGES = {1293--1298},
      ISSN = {0002-9904},
   MRCLASS = {57.10},
  MRNUMBER = {0253350},
MRREVIEWER = {R. E. Stong},
       DOI = {10.1090/S0002-9904-1969-12401-8},
       URL = {http://dx.doi.org/10.1090/S0002-9904-1969-12401-8},
}

@article {RavenelCohomologyStabAlgs,
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   JOURNAL = {Math. Z.},
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    VOLUME = {152},
      YEAR = {1977},
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MRREVIEWER = {A. Liulevicius},
       DOI = {10.1007/BF01488970},
       URL = {http://dx.doi.org/10.1007/BF01488970},
}

@book {RavenelGreenBook,
    AUTHOR = {Ravenel, Douglas C.},
     TITLE = {Complex cobordism and stable homotopy groups of spheres},
    SERIES = {Pure and Applied Mathematics},
    VOLUME = {121},
 PUBLISHER = {Academic Press Inc.},
   ADDRESS = {Orlando, FL},
      YEAR = {1986},
     PAGES = {xx+413},
      ISBN = {0-12-583430-6; 0-12-583431-4},
   MRCLASS = {55-02 (55Qxx 57-02)},
  MRNUMBER = {860042 (87j:55003)},
MRREVIEWER = {Joseph Neisendorfer},
}

@incollection {RavenelObit,
    AUTHOR = {Ravenel, Douglas C.},
     TITLE = {Life after the telescope conjecture},
 BOOKTITLE = {Algebraic {$K$}-theory and algebraic topology ({L}ake
              {L}ouise, {AB}, 1991)},
    SERIES = {NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.},
    VOLUME = {407},
     PAGES = {205--222},
 PUBLISHER = {Kluwer Acad. Publ., Dordrecht},
      YEAR = {1993},
   MRCLASS = {55P42 (19D99 55P60)},
  MRNUMBER = {1367299},
       URL = {https://doi.org/10.1007/978-94-017-0695-7_10},
}

@article {RavenelLocalizationWRTPeriodic,
    AUTHOR = {Ravenel, Douglas C.},
     TITLE = {Localization with respect to certain periodic homology
              theories},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {106},
      YEAR = {1984},
    NUMBER = {2},
     PAGES = {351--414},
      ISSN = {0002-9327},
     CODEN = {AJMAAN},
   MRCLASS = {55P42},
  MRNUMBER = {737778 (85k:55009)},
MRREVIEWER = {J. F. Adams},
       DOI = {10.2307/2374308},
       URL = {http://dx.doi.org/10.2307/2374308},
}

@inproceedings{RavenelNonexistenceArfInvariantElts,
  title={The non-existence of odd primary {A}rf invariant elements in stable homotopy},
  author={Ravenel, Douglas C},
  booktitle={Mathematical Proceedings of the Cambridge Philosophical Society},
  volume={83},
  number={3},
  pages={429--443},
  year={1978},
  organization={Cambridge University Press}
}

@book {RavenelOrangeBook,
    AUTHOR = {Ravenel, Douglas C.},
     TITLE = {Nilpotence and periodicity in stable homotopy theory},
    SERIES = {Annals of Mathematics Studies},
    VOLUME = {128},
      NOTE = {Appendix C by Jeff Smith},
 PUBLISHER = {Princeton University Press, Princeton, NJ},
      YEAR = {1992},
     PAGES = {xiv+209},
      ISBN = {0-691-02572-X},
   MRCLASS = {55P42 (55N22 55Q10 57R77)},
  MRNUMBER = {1192553 (94b:55015)},
MRREVIEWER = {N. J. Kuhn},
}

@incollection {RavenelNovicesGuide,
    AUTHOR = {Ravenel, Douglas C.},
     TITLE = {A novice's guide to the {A}dams-{N}ovikov spectral sequence},
 BOOKTITLE = {Geometric applications of homotopy theory ({P}roc. {C}onf.,
              {E}vanston, {I}ll., 1977), {II}},
    SERIES = {Lecture Notes in Math.},
    VOLUME = {658},
     PAGES = {404--475},
 PUBLISHER = {Springer, Berlin},
      YEAR = {1978},
   MRCLASS = {55T15 (55N22 55Q45)},
  MRNUMBER = {513586},
MRREVIEWER = {J. F. Adams},
}

@article {RavenelWilsonHopfRingForMU,
    AUTHOR = {Ravenel, Douglas C. and Wilson, W. Stephen},
     TITLE = {The {H}opf ring for complex cobordism},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {9},
      YEAR = {1976/77},
    NUMBER = {3},
     PAGES = {241--280},
      ISSN = {0022-4049},
   MRCLASS = {55B20 (57D90)},
  MRNUMBER = {0448337 (56 \#6644)},
MRREVIEWER = {J. F. Adams},
}

@article {RavenelWilsonKthyOfEMSpaces,
    AUTHOR = {Ravenel, Douglas C. and Wilson, W. Stephen},
     TITLE = {The {M}orava {$K$}-theories of {E}ilenberg-{M}ac {L}ane spaces
              and the {C}onner-{F}loyd conjecture},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {102},
      YEAR = {1980},
    NUMBER = {4},
     PAGES = {691--748},
      ISSN = {0002-9327},
     CODEN = {AJMAAN},
   MRCLASS = {55N20 (55P20 55T20 57R85)},
  MRNUMBER = {584466 (81i:55005)},
MRREVIEWER = {J. F. Adams},
       DOI = {10.2307/2374093},
       URL = {http://dx.doi.org/10.2307/2374093},
}

@article {RWY,
    AUTHOR = {Ravenel, Douglas C. and Wilson, W. Stephen and Yagita,
              Nobuaki},
     TITLE = {Brown-{P}eterson cohomology from {M}orava {$K$}-theory},
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  FJOURNAL = {$K$-Theory. An Interdisciplinary Journal for the Development,
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    VOLUME = {15},
      YEAR = {1998},
    NUMBER = {2},
     PAGES = {147--199},
      ISSN = {0920-3036},
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  MRNUMBER = {1648284},
MRREVIEWER = {David C. Johnson},
       DOI = {10.1023/A:1007776725714},
       URL = {http://dx.doi.org/10.1023/A:1007776725714},
}

@ARTICLE{RezkFelixKlein,
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}

@ARTICLE{RezkKoszul,
   author = {{Rezk}, C.},
    title = "{Rings of power operations for Morava E-theories are Koszul}",
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archivePrefix = "arXiv",
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 primaryClass = "math.AT",
 keywords = {Mathematics - Algebraic Topology, 55S25 (Primary), 55S12 (Secondary)},
     year = 2012,
    month = apr,
   adsurl = {http://adsabs.harvard.edu/abs/2012arXiv1204.4831R},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@article {RezkLogarithm,
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   JOURNAL = {J. Amer. Math. Soc.},
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@ARTICLE{RezkNotesOnHMThm,
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@ARTICLE{Rezk512Notes,
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@book {Rudyak,
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MRREVIEWER = {Donald M. Davis},
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@incollection {Sadofsky,
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@article{Salch,
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@article {SchlankStapleton,
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}

@article {Schoeller,
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   MRCLASS = {13.50 (18.00)},
  MRNUMBER = {0281709},
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@article{SchwaenzlRolandVogt,
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@incollection {Segal,
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 BOOKTITLE = {Symposia {M}athematica, {V}ol. {IV} ({INDAM}, {R}ome,
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     PAGES = {377--387},
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@article{SegalEll,
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@ARTICLE{Senger,
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archivePrefix = "arXiv",
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 primaryClass = "math.AT",
 keywords = {Mathematics - Algebraic Topology, 55P43},
     year = 2017,
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   adsurl = {http://adsabs.harvard.edu/abs/2017arXiv171009822S},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article {Shay,
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@article {Shimomura,
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@incollection {ShimomuraYabeM20,
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 BOOKTITLE = {Topology and representation theory ({E}vanston, {IL}, 1992)},
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    VOLUME = {158},
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}

@article {ShimomuraYabeL2S,
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@book {SilvermanAdvanced,
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@article {Singer,
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}

@ARTICLE{SprangNaumann,
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  journal = {ArXiv e-prints},
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 primaryClass = "math.AT",
 keywords = {Mathematics - Algebraic Topology, 55P42, 55P43},
     year = 2014,
    month = sep,
   adsurl = {http://adsabs.harvard.edu/abs/2014arXiv1409.5314S},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@misc{stacks-project,
  shorthand    = {Stacks},
  author       = {The {Stacks Project Authors}},
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@article{Stapleton,
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@Article{StapletonTwisted,
author="Stapleton, Nathaniel",
title="Transchromatic twisted character maps",
journal="Journal of Homotopy and Related Structures",
year="2015",
month="Mar",
day="01",
volume="10",
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pages="29--61",
issn="1512-2891",
doi="10.1007/s40062-013-0040-9",
url="https://doi.org/10.1007/s40062-013-0040-9"
}

@article{SteenrodCyclic,
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@article{SteenrodSymmetric,
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@article {Stojanoska,
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  MRNUMBER = {2946825},
MRREVIEWER = {Paul G. Goerss},
}

@article{Stolz,
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@article{StolzTeichnerWhatIs,
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@article{StolzTeichnerSusy,
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@article {Stong,
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@misc{StricklandBottPeriodicity,
  author = {Strickland, Neil},
  title = {{B}ott Periodicity and {H}opf Rings},
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}

@article {StricklandEthyOfBSigma,
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     TITLE = {Morava {$E$}-theory of symmetric groups},
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       URL = {http://dx.doi.org/10.1016/S0040-9383(97)00054-2},
}

@article {StricklandFiniteSubgps,
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}

@misc{StricklandFGNotes,
  author       = {Strickland, Neil P.},
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  year         = {2006},
}

@incollection {StricklandFSFG,
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 BOOKTITLE = {Homotopy invariant algebraic structures ({B}altimore, {MD},
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    SERIES = {Contemp. Math.},
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   MRCLASS = {55N22 (14L05 18G99 55N34)},
  MRNUMBER = {1718087 (2000j:55011)},
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@article{StricklandFSKS,
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@incollection {StricklandFPFP,
    AUTHOR = {Strickland, Neil P.},
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}

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}

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@phdthesis{Stroilova,
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  school={Massachusetts Institute of Technology}
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@article {ThomasonWilson,
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}

@ARTICLE{Thompson,
   author = {{Thompson}, R.},
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  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
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 primaryClass = "math.AT",
 keywords = {Mathematics - Algebraic Topology, 55N20, 55T15, 55Q51},
     year = 2014,
    month = sep,
   adsurl = {http://adsabs.harvard.edu/abs/2014arXiv1409.3890T},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article {Torii5,
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       URL = {http://dx.doi.org/10.2140/pjm.2011.250.439},
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@article {Torii4,
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       DOI = {10.1007/s00209-009-0605-9},
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}

@article {Torii3,
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  FJOURNAL = {Transactions of the American Mathematical Society},
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   MRCLASS = {55N22 (14L05 55N20)},
  MRNUMBER = {2661512 (2012c:55007)},
MRREVIEWER = {Niko Naumann},
       DOI = {10.1090/S0002-9947-2010-05194-3},
       URL = {http://dx.doi.org/10.1090/S0002-9947-2010-05194-3},
}

@inproceedings {Torii2,
    AUTHOR = {Torii, Takeshi},
     TITLE = {Milnor operations and the generalized {C}hern character},
 BOOKTITLE = {Proceedings of the {N}ishida {F}est ({K}inosaki 2003)},
    SERIES = {Geom. Topol. Monogr.},
    VOLUME = {10},
     PAGES = {383--421},
 PUBLISHER = {Geom. Topol. Publ., Coventry},
      YEAR = {2007},
   MRCLASS = {55N22 (55N20 55S05)},
  MRNUMBER = {2402795 (2009f:55004)},
MRREVIEWER = {Geoffrey M. L. Powell},
       DOI = {10.2140/gtm.2007.10.383},
       URL = {http://dx.doi.org/10.2140/gtm.2007.10.383},
}

@article {Torii1,
    AUTHOR = {Torii, Takeshi},
     TITLE = {On degeneration of one-dimensional formal group laws and
              applications to stable homotopy theory},
   JOURNAL = {Amer. J. Math.},
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      YEAR = {2003},
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MRREVIEWER = {Mark Hovey},
}

@book {Vakil,
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@incollection {Vistoli,
    AUTHOR = {Vistoli, Angelo},
     TITLE = {Grothendieck topologies, fibered categories and descent
              theory},
 BOOKTITLE = {Fundamental algebraic geometry},
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 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2005},
   MRCLASS = {14F20 (14A20)},
  MRNUMBER = {2223406},
}

@ARTICLE{Walker,
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  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
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 primaryClass = "math.AT",
 keywords = {Mathematics - Algebraic Topology, Mathematics - Number Theory, 55P43, 55N22, 14L05},
     year = 2009,
    month = apr,
   adsurl = {http://adsabs.harvard.edu/abs/2009arXiv0905.0022W},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@phdthesis{Wang,
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  author={Wang, Guozhen},
  year={2015},
  school={Massachusetts Institute of Technology}
}

@book {Weil,
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@article{WeilTheta,
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@misc{Weinstein,
  author       = {Weinstein, Jared},
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  year         = {2011},
}

@book {Wilson,
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 PUBLISHER = {Conference Board of the Mathematical Sciences},
   ADDRESS = {Washington, D.C.},
      YEAR = {1982},
     PAGES = {v+86},
      ISBN = {0-8219-1699-3},
   MRCLASS = {55N22 (55P20 55P42 55Q45 55S25)},
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MRREVIEWER = {Franklin P. Peterson},
}

@article {WilsonThesisI,
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     PAGES = {45--55; corrigendum, ibid. 48 (1973), 194},
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       DOI = {10.1007/BF02566110},
       URL = {http://dx.doi.org/10.1007/BF02566110},
}

@article {WilsonThesisII,
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       URL = {http://dx.doi.org/10.2307/2373662},
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@article {WittenEllipticGeneraQFT,
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       URL = {http://projecteuclid.org/euclid.cmp/1104117076},
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@incollection {WittenIndexDiracOperatorLoopSpace,
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    SERIES = {Lecture Notes in Math.},
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  MRNUMBER = {970288},
       DOI = {10.1007/BFb0078045},
       URL = {http://dx.doi.org/10.1007/BFb0078045},
}

@article {Yagita,
    AUTHOR = {Yagita, Nobuaki},
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       URL = {http://dx.doi.org/10.1112/jlms/s2-22.3.423},
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@article {Yu,
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    VOLUME = {96},
      YEAR = {1995},
    NUMBER = {3},
     PAGES = {293--321},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {11S31 (14L05)},
  MRNUMBER = {1327148},
       URL = {http://www.numdam.org/item?id=CM_1995__96_3_293_0},
}

@ARTICLE{Zhu,
   author = {{Zhu}, Y.},
    title = "{Norm coherence for descent of level structures on formal deformations}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1706.03445},
 primaryClass = "math.AT",
 keywords = {Mathematics - Algebraic Topology, Mathematics - Algebraic Geometry, Mathematics - Number Theory},
     year = 2017,
    month = jun,
   adsurl = {http://adsabs.harvard.edu/abs/2017arXiv170603445Z},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@book {ZinkCartierTheory,
    AUTHOR = {Zink, Thomas},
     TITLE = {Cartiertheorie kommutativer formaler {G}ruppen},
    SERIES = {Teubner-Texte zur Mathematik [Teubner Texts in Mathematics]},
    VOLUME = {68},
      NOTE = {With English, French and Russian summaries},
 PUBLISHER = {BSB B. G. Teubner Verlagsgesellschaft, Leipzig},
      YEAR = {1984},
     PAGES = {124},
   MRCLASS = {14L05},
  MRNUMBER = {767090},
MRREVIEWER = {Hans-J\~A${}^1\!/\!_4$rgen Schneider},
}

@article {ZinkDisplays,
    AUTHOR = {Zink, Thomas},
     TITLE = {The display of a formal {$p$}-divisible group},
      NOTE = {Cohomologies $p$-adiques et applications arithm\'etiques, I},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {278},
      YEAR = {2002},
     PAGES = {127--248},
      ISSN = {0303-1179},
   MRCLASS = {14L05 (14F30)},
  MRNUMBER = {1922825},
MRREVIEWER = {Oliver B\~A${}^1\!/\!_4$ltel},
}