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This is a Quantitative Study study.

October 3, 2025Open Access

Prismatic cohomology and A_-cohomology with coefficients

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This article demonstrates the isomorphism between prismatic cohomology and A_inf-cohomology, indicating a new way to approach locally free modules.

The study confirms that prismatic cohomology is isomorphic to A_inf-cohomology for locally finite free crystals.
Key evidence shows the compatibility with inverse image functors and scalar extensions under Frobenius.
The method involves analyzing the structures on the proétale site of the generic fiber.
The findings highlight the utility of q-Higgs modules in understanding these cohomological relationships.

Takeshi Tsuji (2025) studied this question.

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This article demonstrates the isomorphism between prismatic cohomology and A_inf-cohomology, indicating a new way to approach locally free modules.