The level 1 weight 2 case of Serre's conjecture

Luis Victor Dieulefait (1)

1 Dept. Algebra i Geometria

We prove Serre's conjecture for the case of Galois representations of Serre's weight 2 and level 1. We do this by combining the potential modularity results of Taylor and lowering the level for Hilbert modular forms with a Galois descent argument, properties of universal deformation rings, and the non-existence of p-adic Barsotti-Tate conductor 1 Galois representations that we proved in a previous paper.

Mots clés: Galois representations; modular forms

Domaines: Théorie des nombres [math.NT]

Luis Victor Dieulefait. The level 1 weight 2 case of Serre's conjecture. 2007. ⟨hal-00144152⟩