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arXiv · 2411.11084

Integral filtered Sen theory and applications

Hui Gao·Tong Liu
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Abstract

We study Nygaard-, conjugate-, and Hodge filtrations on the many variants of Breuil--Kisin modules associated to integral semi-stable Galois representations. This leads to an integral Sen operator satisfying certain ``$1$-degree shrinking" on the increasing conjugate filtration, and (in special cases) a mod $p$ Sen operator satisfying certain ``$p$-degree shrinking". These constructions are related with prismatic $F$-crystals, Hodge--Tate crystals and $F$-gauges, and have explicit relations with classical (non-prismatic) operators. As applications, we obtain vanishing and torsion bound results on graded of the integral Hodge filtration; our explicit methods also recover results of Gee--Kisin and Bhatt--Gee--Kisin concerning the mod $p$ Hodge filtrations and Frobenius structures.

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Hui Gao, Tong Liu. 2024-11-17. Integral filtered Sen theory and applications. https://arxiv.org/abs/2411.11084

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