La conjecture de modularité de Serre : le cas de conducteur 1
Séminaire Bourbaki : volume 2005/2006, exposés 952-966, Astérisque, no. 311 (2007), Exposé no. 956, pp. 99-122.

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.

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.

Classification : 11F11,  11F80
Mots clés : formes modulaires, représentations galoisiennes
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     title = {La conjecture de modularit\'e de Serre : le cas de conducteur <span class="mathjax-formula">$1$</span>},
     booktitle = {S\'eminaire Bourbaki : volume 2005/2006, expos\'es 952-966},
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Wintenberger, Jean-Pierre. La conjecture de modularité de Serre : le cas de conducteur $1$, dans Séminaire Bourbaki : volume 2005/2006, exposés 952-966, Astérisque, no. 311 (2007), Exposé no. 956, pp. 99-122. http://archive.numdam.org/item/SB_2005-2006__48__99_0/

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