Relative $A_{\rm inf}$-cohomology

Ildar Gaisin; Teruhisa Koshikawa

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arXiv · 2206.07983

Relative $A_{\rm inf}$-cohomology

Ildar Gaisin·Teruhisa Koshikawa

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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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Ildar Gaisin, Teruhisa Koshikawa. 2022-06-16. Relative $A_{\rm inf}$-cohomology. https://arxiv.org/abs/2206.07983

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