2024/11/17 by Gao, Hui, Liu, Tong
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2411.11084
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.