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Relative $A_{\rm inf}$-cohomology (2206.07983v1)
Published 16 Jun 2022 in math.NT and math.AG
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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