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Comptes Rendus Mathématique
Volume 350, n° 9-10
pages 443-448 (mai 2012)
Doi : 10.1016/j.crma.2012.04.012
Received : 29 Mars 2012 ;  accepted : 17 April 2012
Une représentation galoisienne universelle attachée aux formes modulaires modulo 2
A universal Galois representation attached to modular forms modulo 2
 

Joël Bellaïche
Brandeis University, 415 South Street, Waltham, MA 02454-9110, États-Unis 

Résumé

Soit A lʼalgèbre des opérateurs de Hecke agissant sur les formes modulaires paraboliques modulo 2 de niveau 1 et de tous poids. Nicolas et Serre ont déterminé la structure de A : on a  . Soit   le groupe de Galois de lʼextension maximale de   non-ramifiée hors de 2 et lʼinfini, et G son plus grand pro-2-quotient. On construit une représentation galoisienne continue   telle que   pour tout p premier impair. On montre aussi son unicité et on étudie ses propriétés de réductibilité.

The full text of this article is available in PDF format.
Abstract

Let A be the algebra of Hecke operators acting on mod 2 cusp forms of level 1 and any weight. Nicolas and Serre have determined the structure of A : one has  . Let   be the Galois group of the maximal extension of   unramified outside 2 and ∞, and let G be its maximal pro-2-quotient. One constructs a continuous Galois representation   such that   for all odd prime p . One also proves its uniqueness and one studies its irreducibility properties.

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