Adjoint Selmer groups of automorphic Galois representations of unitary type
James Newton
King’s College London; University of Oxford, UKJack A. Thorne
University of Cambridge, UK
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Abstract
Let be the -adic Galois representation attached to a cuspidal, regular algebraic automorphic representation of of unitary type. Under very mild hypotheses on , we prove the vanishing of the (Bloch–Kato) adjoint Selmer group of . We obtain definitive results for the adjoint Selmer groups associated to non-CM Hilbert modular forms and elliptic curves over totally real fields.
Cite this article
James Newton, Jack A. Thorne, Adjoint Selmer groups of automorphic Galois representations of unitary type. J. Eur. Math. Soc. 25 (2023), no. 5, pp. 1919–1967
DOI 10.4171/JEMS/1228