Actions infinitésimales dans la correspondance de Langlands locale p-adique

Abstract

Let V be a two-dimensional absolutely irreducible p-adic Galois representation and let Pi be the p-adic Banach space representation associated to V via Colmez's p-adic Langlands correspondence. We establish a link between the infinitesimal action of GL_2(Q_p) on the locally analytic vectors of Pi, the differential equation associated to V via the theory of Fontaine and Berger, and the Sen polynomial of V. This answers a question of Harris and gives a new proof of a theorem of Colmez: Pi has nonzero locally algebraic vectors if and only if V is potentially semi-stable with distinct Hodge-Tate weights.

Completely revised version, to appear in Math. Annalen

References in corpus (1)

• Endomorphism algebras of admissible p-adic representations of p-adic Lie groups

Cited by in corpus (5)

• Complétés universels de représentations de GL_2(Q_p)
• The p-adic local Langlands correspondence for GL_2(Q_p)
• Extensions de représentations de de Rham et vecteurs localement algébriques
• Revêtements du demi-plan de Drinfeld et correspondance de Langlands p-adique
• Une factorisation de la cohomologie complétée et du système de Beilinson-Kato