On the vanishing of adjoint Bloch–Kato Selmer groups of irreducible automorphic Galois representations

Let $\rho$ be the $p$-adic Galois representation attached to a cuspidal, regular algebraic, polarizable automorphic representation of $\mathrm{GL}_n$. Assuming only that $\rho$ satisfies an irreducibility condition, we prove the vanishing of the adjoint Bloch–Kato Selmer group attached to $\rho$. This generalizes previous work of the author and James Newton.

Full Text (PDF format)

The author’s work received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 714405).

Received 10 March 2021

Received revised 2 February 2022

Accepted 6 March 2022

Published 12 January 2023