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arxiv: 2404.14622 · v2 · submitted 2024-04-22 · 🧮 math.NT

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On local Galois deformation rings: generalised reductive groups

Julian Quast, Vytautas Pa\v{s}k\=unas

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classification 🧮 math.NT
keywords deformationgroupscompletegaloisgeneralisedreductiveringsadic
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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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Cited by 1 Pith paper

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  1. Congruences of first syntomic cohomology groups

    math.NT 2026-05 unverdicted novelty 7.0

    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.