Pointwise criteria of p-adic local systems
Algebraic Geometry
2024-10-21 v1 Number Theory
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.
Cite
@article{arxiv.2409.19742,
title = {Pointwise criteria of p-adic local systems},
author = {Haoyang Guo and Ziquan Yang},
journal= {arXiv preprint arXiv:2409.19742},
year = {2024}
}
Comments
86 pages, comments are very welcome!