Shows the relationship between A_inf cohomology and prismatic theory, suggesting new applications in mathematics.
We construct a relative version of the A inf A_ inf upper A Subscript 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 étale comparison of the q -crystalline pushforward after inverting μ ∈ A inf μ ∈ A_ inf mu element of upper A Subscript inf .
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Gaisin et al. (2026) studied this question.
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