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On the density of supercuspidal points of fixed regular weight in local deformation rings and global Hecke algebras

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arxiv 1809.06598 v3 pith:J4DR3NAT submitted 2018-09-18 math.NT

Matthew Emerton , Vytautas Paskunas This is my paper · ORCID
classification math.NT
keywords deformationalgebrasclosureglobalheckelocalpointsrings
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abstract

We study the Zariski closure of points in local deformation rings corresponding to potential semi-stable representations with certain prescribed $p$-adic Hodge theoretic properties. We show in favourable cases that the closure is equal to a union of irreducible components of the deformation space. We also study an analogous question for global Hecke algebras.

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  1. On the modularity of 2-adic potentially semi-stable deformation rings

    math.NT 2019-08 conditional novelty 7.0 of 10

    For p=2, the support of patched modules meets every irreducible component of the potentially semi-stable deformation ring, yielding the Breuil-Mezard conjecture in the case where the residual representation is a twist...

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