[The conjecture of modularity of Serre: the case of conductor ]
The conjecture says that an irreducible continuous odd representation of the Galois group of in a -dimensional vector space over a finite field comes from a modular form. C. Khare just proved it in the case where the representation is unramified outside the characteristic of .
La conjecture dit qu’une représentation continue irréductible impaire du groupe de Galois de dans un espace vectoriel de dimension sur un corps fini de caractéristique provient d’une forme modulaire. C. Khare vient de la prouver pour les représentations qui sont non ramifiées hors de .
Mot clés : formes modulaires, représentations galoisiennes
Keywords: modular forms, Galois representations
@incollection{SB_2005-2006__48__99_0, author = {Wintenberger, Jean-Pierre}, title = {La conjecture de modularit\'e de {Serre} : le cas de conducteur $1$}, booktitle = {S\'eminaire Bourbaki : volume 2005/2006, expos\'es 952-966}, series = {Ast\'erisque}, note = {talk:956}, pages = {99--122}, publisher = {Soci\'et\'e math\'ematique de France}, number = {311}, year = {2007}, mrnumber = {2359041}, zbl = {1200.11036}, language = {fr}, url = {http://archive.numdam.org/item/SB_2005-2006__48__99_0/} }
TY - CHAP AU - Wintenberger, Jean-Pierre TI - La conjecture de modularité de Serre : le cas de conducteur $1$ BT - Séminaire Bourbaki : volume 2005/2006, exposés 952-966 AU - Collectif T3 - Astérisque N1 - talk:956 PY - 2007 SP - 99 EP - 122 IS - 311 PB - Société mathématique de France UR - http://archive.numdam.org/item/SB_2005-2006__48__99_0/ LA - fr ID - SB_2005-2006__48__99_0 ER -
%0 Book Section %A Wintenberger, Jean-Pierre %T La conjecture de modularité de Serre : le cas de conducteur $1$ %B Séminaire Bourbaki : volume 2005/2006, exposés 952-966 %A Collectif %S Astérisque %Z talk:956 %D 2007 %P 99-122 %N 311 %I Société mathématique de France %U http://archive.numdam.org/item/SB_2005-2006__48__99_0/ %G fr %F SB_2005-2006__48__99_0
Wintenberger, Jean-Pierre. La conjecture de modularité de Serre : le cas de conducteur $1$, in Séminaire Bourbaki : volume 2005/2006, exposés 952-966, Astérisque, no. 311 (2007), Talk no. 956, pp. 99-122. http://archive.numdam.org/item/SB_2005-2006__48__99_0/
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