Socle localement analytique I  [ Locally analytic socle I ]
Annales de l'Institut Fourier, Volume 66 (2016) no. 2, p. 633-685
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.
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.
Received : 2013-10-22
Revised : 2015-03-18
Accepted : 2015-09-10
Published online : 2016-02-17
DOI : https://doi.org/10.5802/aif.3021
Classification:  11S23,  22E35,  22E50
Keywords: Locally analytic representation, Hodge filtration, socle
@article{AIF_2016__66_2_633_0,
     author = {Breuil, Christophe},
     title = {Socle localement analytique I},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {2},
     year = {2016},
     pages = {633-685},
     doi = {10.5802/aif.3021},
     language = {fr},
     url = {https://aif.centre-mersenne.org/item/AIF_2016__66_2_633_0}
}
Socle localement analytique I. Annales de l'Institut Fourier, Volume 66 (2016) no. 2, pp. 633-685. doi : 10.5802/aif.3021. https://aif.centre-mersenne.org/item/AIF_2016__66_2_633_0/

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