The level $1$ weight $2$ case of Serre's conjecture
Luis Dieulefait
Source: Rev. Mat. Iberoamericana Volume 23, Number 3
(2007), 1115-1124.
Abstract
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].
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Permanent link to this document: http://projecteuclid.org/euclid.rmi/1204128312
Mathematical Reviews number (MathSciNet): MR2414504
Zentralblatt MATH identifier: 05281242
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