Congruences of first syntomic cohomology groups
Number Theory
2026-05-12 v1
Abstract
Let O_K be the ring of integers of a finite extension K of Q_p. Given two reflexive F-gauges on O_K, we show that for large enough n, the mod p^n-reductions of their first syntomic cohomology groups, which might be regarded as a refinement of local Bloch--Kato Selmer groups, are isomorphic if and only if the mod p^{2n}-reductions of their attached Breuil--Kisin modules with G_K-actions and Nygaard filtrations are isomorphic.
Keywords
Cite
@article{arxiv.2605.09987,
title = {Congruences of first syntomic cohomology groups},
author = {Yu Min},
journal= {arXiv preprint arXiv:2605.09987},
year = {2026}
}