Serre's modularity conjecture: The level one case
Khare, Chandrashekhar
Duke Math. J., Tome 131 (2006) no. 1, p. 557-589 / Harvested from Project Euclid
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We prove the level one case of Serre's conjecture. Namely, we prove that any continuous, odd, irreducible representation $\overline{\rho}:G_\mathbb{Q} \rightarrow \mathrm{GL}_2(\overline{\mathbb{F}_{p}})$ which is unramified outside $p$ arises from a cuspidal eigenform in $S_{k}(\mathrm{SL}_2(\mathbb{Z}))$ for some integer $k \geq 2$ . The proof relies on the methods introduced in an earlier joint work with J.-P. Wintenberger [31] together with a new method of weight reduction
Publié le : 2006-09-15
Classification:  11F80,  11F11,  11R39 
@article{1156771903,
     author = {Khare, Chandrashekhar},
     title = {Serre's modularity conjecture: The level one case},
     journal = {Duke Math. J.},
     volume = {131},
     number = {1},
     year = {2006},
     pages = { 557-589},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1156771903}
}

Khare, Chandrashekhar. Serre's modularity conjecture: The level one case. Duke Math. J., Tome 131 (2006) no. 1, pp.  557-589. http://gdmltest.u-ga.fr/item/1156771903/