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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.

  • On representations of spinor genera

  • Wai Kiu Chan, Fei Xu
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 2 / March 2004
    Published online by Cambridge University Press:
    04 December 2007, pp. 287-300
    Print publication:
    March 2004
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  • We determine exactly when a quadratic form is represented by a spinor genus of another quadratic form of three or four variables. We apply this to extend the embedding theorem for quaternion and also answer a question by Borovoi.