Revista Matemática Iberoamericana

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

Luis Dieulefait

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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].

Article information

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

Dates
First available in Project Euclid: 27 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1204128312

Mathematical Reviews number (MathSciNet)
MR2414504

Zentralblatt MATH identifier
1171.11032

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

Keywords
Galois representations modular forms

Citation

Dieulefait, Luis. The level $1$ weight $2$ case of Serre's conjecture. Rev. Mat. Iberoamericana 23 (2007), no. 3, 1115--1124. https://projecteuclid.org/euclid.rmi/1204128312


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