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, Tome 33 (2021) no. 3.2, pp. 1115-1141.

Résumé
Abstract

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.

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.

Reçu le : 2019-12-15
Révisé le : 2021-02-15
Accepté le : 2021-06-05
Publié le : 2022-01-26

DOI : 10.5802/jtnb.1191

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

Affiliations des auteurs :

Eric Urban ¹

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

Licence :

CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {On {Euler} systems for adjoint {Hilbert} modular {Galois} representations},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {1115--1141},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
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Eric Urban. On Euler systems for adjoint Hilbert modular Galois representations. Journal de théorie des nombres de Bordeaux, Tome 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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