Congruences of first syntomic cohomology groups
Abstract
Let OK be the ring of integers of a finite extension K of Qp. Given two reflexive F-gauges on OK, we show that for large enough n, the mod pn-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 p2n-reductions of their attached Breuil--Kisin modules with GK-actions and Nygaard filtrations are isomorphic.
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