A prismatic approach to crystalline local systems

2022/03/17 by Guo, Haoyang, Reinecke, Emanuel · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2203.09490

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, Poincaré duality, and Frobenius isogeny.

Cited by

• Syntomification and crystalline local systems
• Finiteness of Heights in Isogeny Classes of Motives with Semistable Reduction

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