Deformations of pseudocharacters and Mazur's finiteness condition

2025/06/12 by Vytautas Paškūnas, Paškūnas, Vytautas, Julian Quast +1
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2506.10901

openalex publication_date 2025/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that deformation rings R^ps of G-pseudocharacters of a profinite group Γ are noetherian, when Γ satisfies Mazur's finiteness condition. The proof proceeds by reduction to the case when Γ is finitely generated, where the result was previously established by the second author. This enables us to extend our work on moduli spaces of R^ps-condensed representations of a finitely generated profinite group Γ, to the groups satisfying Mazur's finiteness condition. We also show that the functor from rigid analytic spaces over ℚ_p to sets, which associates to a rigid space Y the set of continuous O(Y)-valued G-pseudocharacters of Γ is representable by a quasi-Stein rigid analytic space, and we study its general properties. We expect these results to be useful, when studying global Galois representations.

Citations

• Infinitesimal characters and Lafforgue's pseudocharacters
• On local Galois deformation rings: generalised reductive groups
• Pseudorepresentations not arising from genuine representations
• Deformations of G-valued pseudocharacters
• Comparison of different definitions of pseudocharacters
• Morphisms of character varieties
• Moduli of Langlands Parameters
• Coherent sheaves on the stack of Langlands parameters
• G-local systems on smooth projective curves are potentially automorphic
• Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings
• Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale
• Adequate moduli spaces and geometrically reductive group schemes
• The p-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings

Related

• Deformations of G-valued pseudocharacters
• The p-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings
• Effect of increasing the ramification on pseudo-deformation rings
• Simplicial Galois Deformation Functors
• Colength one deformation rings