La conjecture de modularité de Serre : le cas de conducteur $1$

Wintenberger, Jean-Pierre

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 $F$.

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