Adjoint Selmer groups of automorphic Galois representations of unitary type

2019/12/24 by Newton, James, Thorne, Jack A.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1912.11265

Abstract

Let ρ be the p-adic Galois representation attached to a cuspidal, regular algebraic automorphic representation of GL_n of unitary type. Under very mild hypotheses on ρ, we prove the vanishing of the (Bloch--Kato) adjoint Selmer group of ρ. We obtain definitive results for the adjoint Selmer groups associated to non-CM Hilbert modular forms and elliptic curves over totally real fields.

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