Geodesic
The Fontaine-Mazur conjecture for 𝐺𝐿₂
Kisin, Mark1
1 Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
Journal of the American Mathematical Society, Tome 22 (2009) no. 3, pp. 641-690

Voir la notice de l'article provenant de la source American Mathematical Society

We prove new cases of the Fontaine-Mazur conjecture, that a $2$-dimensional $p$-adic representation $\rho$ of $G_{\mathbb {Q}, S}$ which is potentially semi-stable at $p$ with distinct Hodge-Tate weights arises from a twist of a modular eigenform of weight $k\geq 2$. Our approach is via the Breuil-Mézard conjecture, which we prove (many cases of) by combining a global argument with recent results of Colmez and Berger-Breuil on the $p$-adic local Langlands correspondence.
DOI : 10.1090/S0894-0347-09-00628-6

Kisin, Mark 1

1 Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637 
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Kisin, Mark. The Fontaine-Mazur conjecture for 𝐺𝐿₂. Journal of the American Mathematical Society, Tome 22 (2009) no. 3, pp. 641-690. doi: 10.1090/S0894-0347-09-00628-6

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