Adjoint Selmer groups of automorphic Galois representations of unitary type (Q6172670)

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 \(\rho\), the authors prove the vanishing of the (Bloch-Kato) adjoint Selmer group of \(\rho\). They obtain definitive results for the adjoint Selmer groups associated to non-CM Hilbert modular forms and elliptic curves over totally real fields.