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arXiv · 1912.11265

Adjoint Selmer groups of automorphic Galois representations of unitary type

James Newton·Jack A. Thorne
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Abstract

Let $\rho$ be the $p$-adic Galois representation attached to a cuspidal, regular algebraic automorphic representation of $\mathrm{GL}_n$ of unitary type. Under very mild hypotheses on $\rho$, we prove the vanishing of the (Bloch--Kato) adjoint Selmer group of $\rho$. 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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James Newton, Jack A. Thorne. 2019-12-24. Adjoint Selmer groups of automorphic Galois representations of unitary type. https://arxiv.org/abs/1912.11265

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