Adjoint Bloch--Kato Selmer groups of regular algebraic automorphic Galois representations

Lambert A'Campo; Bence Hevesi; Jack A. Thorne; Dmitri Whitmore

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arXiv · 2607.11769

Adjoint Bloch--Kato Selmer groups of regular algebraic automorphic Galois representations

Lambert A'Campo·Bence Hevesi·Jack A. Thorne·Dmitri Whitmore

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Abstract

We prove the vanishing of the adjoint Bloch--Kato Selmer group of the Galois representations associated to regular algebraic automorphic representations of general linear groups over CM fields. A key novelty of our work is that we impose conditions only on the $p$-adic Galois representations, and not on their associated residual representations modulo $p$.

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Lambert A'Campo, Bence Hevesi, Jack A. Thorne, Dmitri Whitmore. 2026-07-13. Adjoint Bloch--Kato Selmer groups of regular algebraic automorphic Galois representations. https://arxiv.org/abs/2607.11769

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