Congruences of first syntomic cohomology groups

Yu Min

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arXiv · 2605.09987

Congruences of first syntomic cohomology groups

Yu Min

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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.

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Yu Min. 2026-05-11. Congruences of first syntomic cohomology groups. https://arxiv.org/abs/2605.09987

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