Actions infinitésimales dans la correspondance de Langlands locale p-adique

Details Actions infinitésimales dans la correspondance de Langlands locale p-adique Actions infinitésimales dans la correspondance de Langlands locale p-adique

2011-02-23

arxiv.org/abs/1102.4788v2

Mathematics

Number Theory

Completely revised version, to appear in Math. Annalen

Scientific paper

10.1007/s00208-011-0736-2 10.100

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.

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