Adjoint Selmer groups of automorphic Galois representations of unitary type

James Newton; Jack A. Thorne

Adjoint Selmer groups of automorphic Galois representations of unitary type

Number Theory 2023-07-03 v3

Authors: James Newton , Jack A. Thorne

Abstract

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 $\rho$ , 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.

Keywords

adjoint selmer group automorphic galois representation unitary type bloch-kato hilbert modular form elliptic curve totally real field

Cite

@article{arxiv.1912.11265,
  title  = {Adjoint Selmer groups of automorphic Galois representations of unitary type},
  author = {James Newton and Jack A. Thorne},
  journal= {arXiv preprint arXiv:1912.11265},
  year   = {2023}
}

Comments

Accepted version -- theorem numbering now matches published version

Adjoint Selmer groups of automorphic Galois representations of unitary type

Abstract

Keywords

Cite

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