Relative $A_{\rm inf}$-cohomology

Ildar Gaisin; Teruhisa Koshikawa

Relative $A_{\rm inf}$-cohomology

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arxiv 2206.07983 v1 pith:OPZOCP52 submitted 2022-06-16 math.NT math.AG

Ildar Gaisin , Teruhisa Koshikawa This is my paper · ORCID

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keywords cohomologyrelativetheoryapplicationbhatt-morrow-scholzebhatt-scholzecomparisonconstruct

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abstract

We construct a relative version of the $A_{\rm inf}$-cohomology theory developed by Bhatt-Morrow-Scholze and relate it to the prismatic theory of Bhatt-Scholze. The construction relies on the fiber product of topoi. As an application we show that there is an \'etale comparison of the $q$-crystalline pushforward after inverting $\mu \in A_{\rm inf}$.

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Prismatic cohomology and $A_{\inf}$-cohomology with coefficients
math.AG 2025-09 conditional novelty 7.0 of 10

Prismatic cohomology of a locally finite free prismatic crystal is canonically isomorphic to A_inf-cohomology of the associated relative Breuil-Kisin-Fargues module, for smooth p-adic formal schemes over the ring of i...

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