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

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

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

Number Theory 2026-07-13 v1

Authors: Lambert A'Campo , Bence Hevesi , Jack A. Thorne , Dmitri Whitmore

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 $p$ .

Keywords

Bloch-Kato Selmer groups adjoint representations automorphic Galois representations CM fields p-adic Galois representations

Cite

@article{arxiv.2607.11769,
  title  = {Adjoint Bloch--Kato Selmer groups of regular algebraic automorphic Galois representations},
  author = {Lambert A'Campo and Bence Hevesi and Jack A. Thorne and Dmitri Whitmore},
  journal= {arXiv preprint arXiv:2607.11769},
  year   = {2026}
}