Serre's modularity conjecture (I)

Chandrashekhar Khare (1) , Jean-Pierre Wintenberger (2)

1 University of Utah
2 IRMA - Institut de Recherche Mathématique Avancée

This paper is the first part of a work which proves Serre's modularity conjecture. We first prove the cases odd p and conductor, modulo 2 Theorems, which are proven in the second part. We then reduce the general case to a modularity statement for 2-adic lifts of modular mod 2 representations ; this statement is now a theorem of Kisin.

Mots clés: Représentations galoisiennes. Formes modulaires; Représentations galoisiennes. Formes modulaires.

Domaines: Théorie des nombres [math.NT]

Chandrashekhar Khare, Jean-Pierre Wintenberger. Serre's modularity conjecture (I). 2007. ⟨hal-00138160⟩