弗拉赫和莫林的猜想

Pub Date : 2024-06-26 DOI:10.1016/j.jnt.2024.05.013

Bruno Chiarellotto , Nicola Mazzari , Yukihide Nakada

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引用次数: 0

摘要

弗拉赫和莫林最近提出的一个猜想将单色性对定义在混合特征DVR上的算术方案的泛纤维的p-adoisic Beilinson-Hyodo-Kato cohomology的伽罗瓦不变部分的作用与（其特殊纤维的）同调联系起来。在给定算术方案的特殊纤维也是正特征曲线上几何族的纤维的情况下，我们证明了这一猜想。

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A conjecture of Flach and Morin

A conjecture recently stated by Flach and Morin relates the action of the monodromy on the Galois invariant part of the p-adic Beilinson–Hyodo–Kato cohomology of the generic fiber of a scheme defined over a DVR of mixed characteristic to (the cohomology of) its special fiber. We prove the conjecture in the case that the special fiber of the given arithmetic scheme is also a fiber of a geometric family over a curve in positive characteristic.

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