On the vanishing of adjoint Bloch--Kato Selmer groups of irreducible automorphic Galois representations

2022/07/11 by Jack A. Thorne, Thorne, Jack A.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2207.04925

openalex publication_date 2022/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ρ be the p-adic Galois representation attached to a cuspidal, regular algebraic, polarizable automorphic representation of GL_n. Assuming only that ρ satisfies an irreducibility condition, we prove the vanishing of the adjoint Bloch--Kato Selmer group attached to ρ. This generalizes previous work of the author and James Newton.

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