For large n, mod p^n reductions of first syntomic cohomology groups of reflexive F-gauges on O_K are isomorphic iff mod p^{2n} reductions of attached Breuil-Kisin modules with G_K-action and Nygaard filtration are isomorphic.
On local Galois deformation rings: generalised reductive groups
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abstract
We study deformation theory of mod $p$ Galois representations of $p$-adic fields with values in generalised reductive group schemes, such as $L$-groups and $C$-groups. We show that the corresponding deformation rings are complete intersections of expected dimension. We determine their irreducible components in many cases and show that they and their special fibres are normal and complete intersection.
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2026 1verdicts
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Congruences of first syntomic cohomology groups
For large n, mod p^n reductions of first syntomic cohomology groups of reflexive F-gauges on O_K are isomorphic iff mod p^{2n} reductions of attached Breuil-Kisin modules with G_K-action and Nygaard filtration are isomorphic.