On Euler systems for adjoint Hilbert modular Galois representations

Eric Urban

doi:10.5802/jtnb.1191

Eric Urban ¹

¹ Department of Mathematics Columbia University 2990 Broadway New York, NY 10027, USA

Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 3.2, pp. 1115-1141.

Abstract
Résumé

We prove the existence of Euler systems for $p$ -ordinary adjoint modular Galois representations using deformations of Galois representations coming from $p$ -ordinary Hilbert modular forms, and relate them to $p$ -adic $L$ -functions under a conjectural formula for the Fitting ideals of some equivariant congruence modules for abelian base change.

Nous prouvons l’existence de systèmes d’Euler pour les représentations galoisiennes modulaires adjointes $p$ -ordinaires en utilisant les déformations de représentations galoisiennes provenant de formes modulaires $p$ -ordinaires de Hilbert et nous leurs associons des fonctions L $p$ -adiques via une formule conjecturale pour l’idéal de Fitting d’un module de congruences équivariant pour le changement de base abélien.

Received: 2019-12-15
Revised: 2021-02-15
Accepted: 2021-06-05
Published online: 2022-01-26

DOI: 10.5802/jtnb.1191

Classification: 11F80, 11F33, 11F41
Keywords: Euler systems, Deformation, Galois representations, Hecke algebra, Hida Theory

Author's affiliations:

Eric Urban ¹

¹ Department of Mathematics Columbia University 2990 Broadway New York, NY 10027, USA

License:

CC-BY-ND 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Eric Urban. On Euler systems for adjoint Hilbert modular Galois representations. Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 3.2, pp. 1115-1141. doi : 10.5802/jtnb.1191. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1191/

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