The conjecture of modularity of Serre: the case of conductor 1

Jean-Pierre Wintenberger

Séminaire Bourbaki (2005-2006)

  • Volume: 48, page 99-122
  • ISSN: 0303-1179

Abstract

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The conjecture says that an irreducible continuous odd representation of the Galois group of Q in a 2 -dimensional vector space over a finite field F comes from a modular form. C. Khare just proved it in the case where the representation is unramified outside the characteristic of F .

How to cite

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Wintenberger, Jean-Pierre. "La conjecture de modularité de Serre : le cas de conducteur $1$." Séminaire Bourbaki 48 (2005-2006): 99-122. <http://eudml.org/doc/252166>.

@article{Wintenberger2005-2006,
abstract = {La conjecture dit qu’une représentation continue irréductible impaire du groupe de Galois de $Q$ dans un espace vectoriel de dimension $2$ sur un corps fini $F$ de caractéristique $p$ provient d’une forme modulaire. C. Khare vient de la prouver pour les représentations qui sont non ramifiées hors de $p$.},
author = {Wintenberger, Jean-Pierre},
journal = {Séminaire Bourbaki},
keywords = {modular forms; Galois representations},
language = {fre},
pages = {99-122},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {La conjecture de modularité de Serre : le cas de conducteur $1$},
url = {http://eudml.org/doc/252166},
volume = {48},
year = {2005-2006},
}

TY - JOUR
AU - Wintenberger, Jean-Pierre
TI - La conjecture de modularité de Serre : le cas de conducteur $1$
JO - Séminaire Bourbaki
PY - 2005-2006
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 48
SP - 99
EP - 122
AB - La conjecture dit qu’une représentation continue irréductible impaire du groupe de Galois de $Q$ dans un espace vectoriel de dimension $2$ sur un corps fini $F$ de caractéristique $p$ provient d’une forme modulaire. C. Khare vient de la prouver pour les représentations qui sont non ramifiées hors de $p$.
LA - fre
KW - modular forms; Galois representations
UR - http://eudml.org/doc/252166
ER -

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