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arXiv · 2405.18245

Prismatic $F$-crystals and Wach modules

Abhinandan
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Abstract

We show that the category of analytic/completed prismatic $F$-crystals on the absolute prismatic site of a small (unramified at $p$) base ring is naturally equivalent to the category of relative Wach modules from the theory of $(\varphi, \Gamma)$-modules. The result is obtained by showing that the data of the Galois action on a Wach module is equivalent to the data of a prismatic stratification on the underlying $\varphi$-module. Along the way, we obtain new descent results for relative Wach modules.

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Abhinandan. 2024-05-28. Prismatic $F$-crystals and Wach modules. https://arxiv.org/abs/2405.18245

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