What question did this study set out to answer?

This research aims to develop a relative version of A_inf cohomology theory and establish its connections to prismatic theory.

July 23, 2026

RELATIVE A inf A {₈₍₅}upper A Subscript inf-COHOMOLOGY

IGIldar GaisinKyoto University TKTeruhisa KoshikawaKeio University

Key Points

This research aims to develop a relative version of A_inf cohomology theory and establish its connections to prismatic theory.
Constructed a relative version of A_inf cohomology theory based on previous work by Bhatt-Morrow-Scholze.
Utilized the fiber product of topoi for theoretical groundwork.
Demonstrated an étale comparison of the q-crystalline pushforward after inverting μ in A_inf.
Established a significant relationship between A_inf cohomology and the prismatic theory.
Showed that the q-crystalline pushforward exhibits the expected étale comparison after appropriate inversions.

Abstract

Abstract We construct a relative version of the A inf A {₈₍₅} 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 A {₈₍₅} mu element of upper A Subscript inf.

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Cite This Study

Gaisin et al. (Tue,) studied this question.

synapsesocial.com/papers/6a61b056faa9903c5116afae https://doi.org/https://doi.org/10.1017/s1474748026101765

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