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Decembar, 2007 The level $1$ weight $2$ case of Serre's conjecture
Luis Dieulefait
Rev. Mat. Iberoamericana 23(3): 1115-1124 (Decembar, 2007).


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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Luis Dieulefait. "The level $1$ weight $2$ case of Serre's conjecture." Rev. Mat. Iberoamericana 23 (3) 1115 - 1124, Decembar, 2007.


Published: Decembar, 2007
First available in Project Euclid: 27 February 2008

zbMATH: 1171.11032
MathSciNet: MR2414504

Primary: 11F11 , 11F80

Keywords: Galois representations , modular forms

Rights: Copyright © 2007 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.23 • No. 3 • Decembar, 2007
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