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arXiv · 2409.19742

Pointwise criteria of p-adic local systems

Haoyang Guo·Ziquan Yang
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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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Haoyang Guo, Ziquan Yang. 2024-09-29. Pointwise criteria of p-adic local systems. https://arxiv.org/abs/2409.19742

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