Geodesic
On Serre’s conjecture for 2-dimensional mod p representations of $\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$
Chandrashekhar Khare1 ; Jean-Pierre Wintenberger2
1 Department of Mathematics<br/>UCLA<br/>Los Angeles, CA 90095<br/>United States
2 Université Louis Pasteur<br/>Département de Mathématique<br/>7, rue Renée Descartes<br/>67084 Strasbourg Cedex<br/>France
Annals of mathematics, Tome 169 (2009) no. 1, pp. 229-253.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove the existence in many cases of minimally ramified $p$-adic lifts of 2-dimensional continuous, odd, absolutely irreducible, mod $p$ representations $\overline{\rho}$ of the absolute Galois group of $\mathbb{Q}$. It is predicted by Serre’s conjecture that such representations arise from newforms of optimal level and weight.
DOI : 10.4007/annals.2009.169.229

Chandrashekhar Khare 1 ; Jean-Pierre Wintenberger 2

1 Department of Mathematics<br/>UCLA<br/>Los Angeles, CA 90095<br/>United States
2 Université Louis Pasteur<br/>Département de Mathématique<br/>7, rue Renée Descartes<br/>67084 Strasbourg Cedex<br/>France 
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     title = {On {Serre{\textquoteright}s} conjecture for 2-dimensional mod p representations of $\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$},
     journal = {Annals of mathematics},
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Chandrashekhar Khare; Jean-Pierre Wintenberger. On Serre’s conjecture for 2-dimensional mod p representations of $\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$. Annals of mathematics, Tome 169 (2009) no. 1, pp. 229-253. doi : 10.4007/annals.2009.169.229. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.169.229/

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