English

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}
}