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

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 $p$.