Adjoint Selmer groups of automorphic Galois representations of unitary type

Source abstract

Let \rho be the p -adic Galois representation attached to a cuspidal, regular algebraic automorphic representation of \operatorname{GL}_n of unitary type. Under very mild hypotheses on \rho , we prove the vanishing of the (Bloch–Kato) adjoint Selmer group of \rho . We obtain definitive results for the adjoint Selmer groups associated to non-CM Hilbert modular forms and elliptic curves over totally real fields.