Soit une extension finie de et un entier . À toute filtration de Hodge de poids de Hodge-Tate distincts sur une représentation de rang suffisamment générique du groupe de Weil-Deligne de , on associe une représentation localement -analytique semi-simple de longueur finie de . On montre plusieurs propriétés de cette représentation. Par exemple, lorsqu’elle possède un réseau stable par , alors la filtration de départ est faiblement admissible.
Let be a finite extension of and a positive integer. To each Hodge filtration with distinct Hodge-Tate weights on an -dimensional sufficiently generic representation of the Weil-Deligne group of , we associate a semi-simple finite length locally -analytic representation of . We show several properties of this representation of . For instance, if it has an invariant lattice, then the starting Hodge filtration is weakly admissible.
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Mot clés : Représentation localement analytique, filtration de Hodge, socle
Keywords: Locally analytic representation, Hodge filtration, socle
Breuil, Christophe 1
@article{AIF_2016__66_2_633_0, author = {Breuil, Christophe}, title = {Socle localement analytique {I}}, journal = {Annales de l'Institut Fourier}, pages = {633--685}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {66}, number = {2}, year = {2016}, doi = {10.5802/aif.3021}, language = {fr}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3021/} }
TY - JOUR AU - Breuil, Christophe TI - Socle localement analytique I JO - Annales de l'Institut Fourier PY - 2016 SP - 633 EP - 685 VL - 66 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3021/ DO - 10.5802/aif.3021 LA - fr ID - AIF_2016__66_2_633_0 ER -
Breuil, Christophe. Socle localement analytique I. Annales de l'Institut Fourier, Tome 66 (2016) no. 2, pp. 633-685. doi : 10.5802/aif.3021. https://aif.centre-mersenne.org/articles/10.5802/aif.3021/
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