Generic smoothness for G-valued potentially semi-stable deformation\n rings

2014/03/06 by Rebecca Bellovin, Bellovin, Rebecca
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1403.1411

openalex publication_date 2014/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We extend Kisin's results on the structure of characteristic 0 Galois\ndeformation rings to deformation rings of Galois representations valued in\narbitrary connected reductive groups G. In particular, we show that such\nGalois deformation rings are complete intersection. In addition, we study\nexplicitly the structure of the moduli space X_\φ,N of (framed)\n(\φ,N)-modules when G= GL_n. We show that when G= GL₃ and\nK₀= Q_p, X_\φ,N has a singular component, and we construct a\nmoduli-theoretic resolution of singularities.\n

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