The level $1$ weight $2$ case of Serre's conjecture
Dieulefait, Luis
Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, p. 1115-1124 / Harvested from Project Euclid
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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].
Publié le : 2007-12-15
Classification:  Galois representations,  modular forms,  11F11,  11F80 
@article{1204128312,
     author = {Dieulefait, Luis},
     title = {The level $1$ weight $2$ case of Serre's conjecture},
     journal = {Rev. Mat. Iberoamericana},
     volume = {23},
     number = {1},
     year = {2007},
     pages = { 1115-1124},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1204128312}
}

Dieulefait, Luis. The level $1$ weight $2$ case of Serre's conjecture. Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, pp.  1115-1124. http://gdmltest.u-ga.fr/item/1204128312/