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.

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
Urban, Eric 1

1 Department of Mathematics Columbia University 2990 Broadway New York, NY 10027, USA
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Urban, Eric. 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. http://www.numdam.org/articles/10.5802/jtnb.1191/

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