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Pointwise criteria of p-adic local systems

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arxiv 2409.19742 v1 pith:L4XMUW6K submitted 2024-09-29 math.AG math.NT

Haoyang Guo , Ziquan Yang This is my paper · ORCID
classification math.AGmath.NT
keywords semi-stablecrystallineresplocalsmoothapplicationsclassicalcomparison
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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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Cited by 3 Pith papers

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  1. Log prismatic $F$-crystals and realization functors

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    Realization functors from log prismatic F-crystals to étale, crystalline, and de Rham categories are constructed for semi-stable formal schemes with horizontal boundary divisors, and the étale realization is proved fu...

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