Potential automorphy of GSpin_2n+1-valued Galois representations

2019/10/08 by Stefan Patrikis, Patrikis, Stefan, Shiang Tang +1
Mathematics · #11F80 #11R39 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1910.03164

openalex publication_date 2019/10/08 · openalex created_date 2019/10/18 · openalex updated_date 2026/07/28

Abstract

We prove a potentially automorphy theorem for suitable Galois representations Γ_F⁺ → GSpin_2n+1(\mathbbF_p) and Γ_F⁺ → GSpin_2n+1(ℚ_p), where Γ_F⁺ is the absolute Galois group of a totally real field F⁺. We also prove results on solvable descent for GSp_2n(\mathbbA_F⁺) and use these to put representations Γ_F⁺ → GSpin_2n+1(ℚ_p) into compatible systems of GSpin_2n+1(ℚ_ℓ)-valued representations.

Citations

• On Euler Products and the Classification of Automorphic Representations I

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