Socle localement analytique I
Annales de l'Institut Fourier, Tome 66 (2016) no. 2, pp. 633-685.

Soit L une extension finie de Q p et n un entier >0. À toute filtration de Hodge de poids de Hodge-Tate distincts sur une représentation de rang n suffisamment générique du groupe de Weil-Deligne de L, on associe une représentation localement Q p -analytique semi-simple de longueur finie de GL n (L). On montre plusieurs propriétés de cette représentation. Par exemple, lorsqu’elle possède un réseau stable par GL n (L), alors la filtration de départ est faiblement admissible.

Let L be a finite extension of Q p and n a positive integer. To each Hodge filtration with distinct Hodge-Tate weights on an n-dimensional sufficiently generic representation of the Weil-Deligne group of L, we associate a semi-simple finite length locally Q p -analytic representation of GL n (L). We show several properties of this representation of GL n (L). For instance, if it has an invariant lattice, then the starting Hodge filtration is weakly admissible.

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DOI : 10.5802/aif.3021
Classification : 11S23, 22E35, 22E50
Mot clés : Représentation localement analytique, filtration de Hodge, socle
Keywords: Locally analytic representation, Hodge filtration, socle
Breuil, Christophe 1

1 Bâtiment 425 C.N.R.S. et Université Paris-Sud 91405 Orsay Cedex France
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Breuil, Christophe. Socle localement analytique I. Annales de l'Institut Fourier, Tome 66 (2016) no. 2, pp. 633-685. doi : 10.5802/aif.3021. http://www.numdam.org/articles/10.5802/aif.3021/

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