On Euler systems for adjoint Hilbert modular Galois representations
Eric Urban1
1Department 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

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:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1191
Classification: 11F80, 11F33, 11F41
Keywords: Euler systems, Deformation, Galois representations, Hecke algebra, Hida Theory

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
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
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