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

James Newton, Jack A. Thorne

University of Cambridge

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Abstract

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

Original language	English
Journal	Journal of the European Mathematical Society
Publication status	Accepted/In press - 16 Jul 2020

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Adjoint Selmer groups of_NEWTON_Accepted16July2020_GREEN AAMAccepted author manuscript, 596 KB
Adjoint Selmer groups of_NEWTON_Accepted16July2020_GREEN AAMAccepted author manuscript, 597 KB

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title = "Adjoint Selmer groups of automorphic Galois representations of unitary type",

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

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AU - Newton, James

AU - Thorne, Jack A.

PY - 2020/7/16

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N2 - Let ρ be the p-adic Galois representation attached to a cuspidal, regular algebraic automorphic representation of GLn of unitary type. Under very mild hypotheses on ρ, we prove the vanishing of the (Bloch–Kato) adjoint Selmer group of ρ. We obtain definitive results for the adjoint Selmer groups associated to non-CM Hilbert modular forms and elliptic curves over totally real fields.

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

UR - https://arxiv.org/pdf/1912.11265.pdf

M3 - Article

SN - 1435-9863

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

ER -

Adjoint Selmer groups of automorphic Galois representations of unitary type

Abstract

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