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2 results

  • Extensions de représentations de de Rham et vecteurs localement algébriques

  • Gabriel Dospinescu
  • Journal:
    Compositio Mathematica / Volume 151 / Issue 8 / August 2015
    Published online by Cambridge University Press:
    03 March 2015, pp. 1462-1498
    Print publication:
    August 2015
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  • Let ${\rm\Pi}$ be an irreducible unitary completion of a locally algebraic $\text{GL}_{2}(\mathbf{Q}_{p})$-representation. We describe those first-order deformations of ${\rm\Pi}$ which are themselves completions of a locally algebraic representation. This answers a question of Paškūnas and has direct applications to the Breuil–Mézard conjecture.

  • Structures de Hodge–Pink pour les φ/𝔖-modules de Breuil et Kisin

  • Part of
  • Alain Genestier, Vincent Lafforgue
  • Journal:
    Compositio Mathematica / Volume 148 / Issue 3 / May 2012
    Published online by Cambridge University Press:
    03 May 2012, pp. 751-789
    Print publication:
    May 2012
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  • In this article, we apply the methods of our work on Fontaine’s theory in equal characteristics to the φ/𝔖-modules of Breuil and Kisin. Thanks to a previous article of Kisin, this yields a new and rather elementary proof of the theorem ‘weakly admissible implies admissible’ of Colmez and Fontaine.