FORMES MODULAIRES DE HILBERT MODULO p ET VALEURS D'EXTENSIONS GALOISIENNES

IF 1.3 1区数学 Q1 MATHEMATICS

Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2012-08-27 DOI:10.24033/asens.2230

C. Breuil, Fred Diamond

引用次数: 32

Abstract

Resume. — Soit F un corps totalement reel, v une place de F non ramifiee di- visant p et ρ : Gal(Q/F) → GL2(Fp) une representation continue irreductible dont la restriction ρ| Gal(Fv/Fv) est reductible et suffisamment generique. Siρ est modu- laire (et satisfait quelques conditions techniques faibles), nous montrons comment retrouver l'extension correspondante entre les deux caracteres de Gal(Fv/Fv) en terme de l'action de GL2(Fv) sur la cohomologie modulo p. Abstract. — Let F be a totally real field, v an unramified place of F dividing p and ρ : Gal(Q/F) → GL2(Fp) a continuous irreducible representation such that ρ| Gal(Fv/Fv) is reducible and sufficiently generic. Ifρ is modular (and satisfies some weak technical assumptions), we show how to recover the corresponding extension between the two characters of Gal(Fv/Fv) in terms of the action of GL2(Fv) on the cohomology mod p.

查看原文本刊更多论文

希尔伯特模形式p模和伽罗sian扩展的值

重新开始-所以F团累加卷，F非微分p = 1， ρ: Gal(Q/F)→GL2(Fp) 1表示继续不可约，不限制ρ| Gal(Fv/Fv)可约，满足泛型。Siρ est模- laire (let satislequques conditions techniques faibles)， nous montrons注释reverver l'extension corresponter中心的双特征de Gal(Fv/Fv)在项上的作用de GL2(Fv) sur la上同调模。-设F是一个全实数域，v是F除以p和ρ的非散化点:Gal(Q/F)→GL2(Fp)是一个连续的不可约表示，使得ρ| Gal(Fv/Fv)是可约的和充分泛型的。如果ρ是模的(并且满足一些弱的技术假设)，我们展示了如何根据GL2(Fv)对上同调模p的作用恢复Gal(Fv/Fv)的两个特征之间的相应扩展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Annales Scientifiques De L Ecole Normale Superieure 数学-数学

CiteScore

3.00

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics. Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition. The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.