Using recent work of Colmez and Berger-Breuil, one can prove both conjectures for representations which becomes semi-stable over an abelian extension.
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The conjectures of Fontaine-Mazur and Breuil-Mezard |
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will explain an intimate connection between the Fontaine-Mazur
conjecture, the Breuil-Mezard conjecture and the p-adic local Langlands
correspondence. Using recent work of Colmez and Berger-Breuil, one can prove both conjectures for representations which becomes semi-stable over an abelian extension. |