The Fontaine-Mazur conjecture for {GL}_2

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The Fontaine-Mazur conjecture for {GL}_2

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Title: The Fontaine-Mazur conjecture for {GL}_2
Author: Kisin, Mark
Citation: Kisin, Mark. 2009. “The Fontaine-Mazur Conjecture for {GL}_2.” Journal of the American Mathematical Society 22, no. 3: 641–690.
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Abstract: We prove new cases of the Fontaine-Mazur conjecture, that a 2 -dimensional p -adic representation rho of G_{{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>= 2 . Our approach is via the Breuil-Mezard 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.
Published Version: doi:10.1090/S0894-0347-09-00628-6
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