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arXiv · 2203.09490

A prismatic approach to crystalline local systems

Haoyang Guo·Emanuel Reinecke
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Abstract

Let X be a smooth p-adic formal scheme. We show that integral crystalline local systems on the generic fiber of X are equivalent to prismatic F-crystals over the analytic locus of the prismatic site of X. As an application, we give a prismatic proof of Fontaine's C_crys-conjecture, for general coefficients, in the relative setting, and allowing ramified base fields. Along the way, we also establish various foundational results for the cohomology of prismatic F-crystals, including various comparison theorems, Poincar\'e duality, and Frobenius isogeny.

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Haoyang Guo, Emanuel Reinecke. 2022-03-17. A prismatic approach to crystalline local systems. https://arxiv.org/abs/2203.09490

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