{"title":"FORMES MODULAIRES DE HILBERT MODULO p ET VALEURS D'EXTENSIONS GALOISIENNES","authors":"C. Breuil, Fred Diamond","doi":"10.24033/asens.2230","DOIUrl":null,"url":null,"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.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"51 1","pages":"905-974"},"PeriodicalIF":1.3000,"publicationDate":"2012-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"32","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Scientifiques De L Ecole Normale Superieure","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.24033/asens.2230","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.
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