Pointwise criteria of p-adic local systems

Haoyang Guo; Ziquan Yang

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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The Tate conjecture for surfaces of geometric genus one -- embracing singularities
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By extending Kuga-Satake period morphisms to singular models, the authors prove the Tate conjecture for many geometric-genus-one surfaces and BSD for height-one elliptic curves over genus-one function fields.

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