Revista Matemática Iberoamericana

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Volume 23, Issue 3, 2007, pp. 1115–1124
DOI: 10.4171/RMI/525

Published online: 2007-12-31

The level 1 weight 2 case of Serre’s conjecture

Luis Victor Dieulefait[1]

(1) Universitat de Barcelona, Spain

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 proved in [Dieulefait, L.: Existence of families of Galois representations and new cases of the Fontaine-Mazur conjecture. J. Reine Angew. Math. 577 (2004), 147-151].

Keywords: Galois representations, modular forms

Dieulefait Luis Victor: The level 1 weight 2 case of Serre’s conjecture. Rev. Mat. Iberoam. 23 (2007), 1115-1124. doi: 10.4171/RMI/525