Goal
Develop the topology and residue-field API of the maximal spectrum of an affinoid algebra.
Suggested scope:
- relate
MaximalSpectrum A to the closed points of PrimeSpectrum A;
- provide the induced Zariski topology and continuity of contravariant pullback;
- package residue fields at maximal ideals and their finite-dimensionality over the ground field;
- expose reusable functoriality lemmas for later rigid-affinoid point constructions.
Build on Rigid/AffinoidAlgebra/MaximalSpectrum.lean and the existing affinoid Nullstellensatz/finite-quotient results. This is independent of the current global-space cores and Tate acyclicity.
Comment claimed before starting.
Goal
Develop the topology and residue-field API of the maximal spectrum of an affinoid algebra.
Suggested scope:
MaximalSpectrum Ato the closed points ofPrimeSpectrum A;Build on
Rigid/AffinoidAlgebra/MaximalSpectrum.leanand the existing affinoid Nullstellensatz/finite-quotient results. This is independent of the current global-space cores and Tate acyclicity.Comment
claimedbefore starting.