Revista Matemática Iberoamericana

The level $1$ weight $2$ case of Serre's conjecture

Luis Dieulefait

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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].

Article information

Rev. Mat. Iberoamericana, Volume 23, Number 3 (2007), 1115-1124.

First available in Project Euclid: 27 February 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F11: Holomorphic modular forms of integral weight 11F80: Galois representations

Galois representations modular forms


Dieulefait, Luis. The level $1$ weight $2$ case of Serre's conjecture. Rev. Mat. Iberoamericana 23 (2007), no. 3, 1115--1124.

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