Geodesic
Moduli of finite flat group schemes, and modularity
Mark Kisin1
1 Department of Mathematics<br/>Harvard University<br/>1 Oxford Street<br/>Cambridge, MA 02138<br/>United States
Annals of mathematics, Tome 170 (2009) no. 3, pp. 1085-1180.

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

We prove that, under some mild conditions, a two dimensional $p$-adic Galois representation which is residually modular and potentially Barsotti-Tate at $p$ is modular. This provides a more conceptual way of establishing the Shimura-Taniyama-Weil conjecture, especially for elliptic curves which acquire good reduction over a wildly ramified extension of $\mathbb Q_3$. The main ingredient is a new technique for analyzing flat deformation rings. It involves resolving them by spaces which parametrize finite flat group scheme models of Galois representations.
DOI : 10.4007/annals.2009.170.1085

Mark Kisin 1

1 Department of Mathematics<br/>Harvard University<br/>1 Oxford Street<br/>Cambridge, MA 02138<br/>United States 
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Mark Kisin. Moduli of finite flat group schemes, and modularity. Annals of mathematics, Tome 170 (2009) no. 3, pp. 1085-1180. doi : 10.4007/annals.2009.170.1085. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.1085/

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