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

Jack A. Thorne

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arXiv · 2207.04925

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

Jack A. Thorne

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Abstract

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

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Jack A. Thorne. 2022-07-11. On the vanishing of adjoint Bloch--Kato Selmer groups of irreducible automorphic Galois representations. https://arxiv.org/abs/2207.04925

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