We prove the existence of Euler systems for -ordinary adjoint modular Galois representations using deformations of Galois representations coming from -ordinary Hilbert modular forms, and relate them to -adic -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 -ordinaires en utilisant les déformations de représentations galoisiennes provenant de formes modulaires -ordinaires de Hilbert et nous leurs associons des fonctions L -adiques via une formule conjecturale pour l’idéal de Fitting d’un module de congruences équivariant pour le changement de base abélien.
Revised:
Accepted:
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Keywords: Euler systems, Deformation, Galois representations, Hecke algebra, Hida Theory
@article{JTNB_2021__33_3.2_1115_0, author = {Urban, Eric}, 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}, volume = {33}, number = {3.2}, year = {2021}, doi = {10.5802/jtnb.1191}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.1191/} }
TY - JOUR AU - Urban, Eric TI - On Euler systems for adjoint Hilbert modular Galois representations JO - Journal de théorie des nombres de Bordeaux PY - 2021 SP - 1115 EP - 1141 VL - 33 IS - 3.2 PB - Société Arithmétique de Bordeaux UR - http://archive.numdam.org/articles/10.5802/jtnb.1191/ DO - 10.5802/jtnb.1191 LA - en ID - JTNB_2021__33_3.2_1115_0 ER -
%0 Journal Article %A Urban, Eric %T On Euler systems for adjoint Hilbert modular Galois representations %J Journal de théorie des nombres de Bordeaux %D 2021 %P 1115-1141 %V 33 %N 3.2 %I Société Arithmétique de Bordeaux %U http://archive.numdam.org/articles/10.5802/jtnb.1191/ %R 10.5802/jtnb.1191 %G en %F JTNB_2021__33_3.2_1115_0
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://archive.numdam.org/articles/10.5802/jtnb.1191/
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