Pointwise criteria of p-adic local systems

2024/09/29 by Guo, Haoyang, Yang, Ziquan
#14F30 #14G45 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2409.19742

Abstract

Given a Z_p-linear local system over a smooth rigid space, we show that it is crystalline (resp. semi-stable) with respect to any smooth (resp. semi-stable) integral model if and only if its restrictions at many classical points are crystalline (resp. semi-stable) representations. To this end, we introduce a crystalline Riemann--Hilbert functor, and give several applications, including a semi-stable comparison theorem in the relative setting.

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