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Annales scientifiques de l'ENS - Parutions - série 4, 44 (2011)

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ANNALES SCIENTIFIQUES DE L’ÉCOLE NORMALE SUPÉRIEURE, série 4 44, fascicule 6 (2011)

Laurent Fargues
La filtration canonique des points de torsion des groupes -divisibles
Annales scientifiques de l'ENS 44, fascicule 6 (2011), 905-961

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Résumé :
Étant donnés un entier et un groupe de Barsotti-Tate tronqué d'échelon et de dimension sur un anneau de valuation d'inégales caractéristiques, nous donnons une borne explicite sur son invariant de Hasse qui implique que sa filtration de Harder-Narasimhan possède un sous-groupe libre de rang . Lorsque n=1 nous redémontrons également le théorème d'Abbes-Mokrane ([120]) et de Tian ([164]) par des méthodes locales. On applique cela aux familles -adiques de tels objets et en particulier à certaines variétés de Shimura de type PEL afin de montrer l'existence de familles compatibles de sections de certaines correspondances de Hecke sur des voisinages tubulaires explicites du lieu ordinaire.

Mots-clefs : Groupes -divisibles, variétés de Shimura

Abstract:
The canonical filtration of the torsion points of -divisible groups
Given an integer and a truncated Barsotti-Tate group of level and dimension over an unequal characteristic valuation ring, we give an explicit bound on its Hasse invariant so that its Harder-Narasimhan filtration has a break which is free of rank . When n=1 we also give a local proof of the Abbes-Mokrane ([120]) and Tian ([164]) theorem. We apply this to -adic families of such objects and, in particular, we prove the existence of compatible families of sections of some Hecke correspondences on explicit tubular neighborhoods of the ordinary locus in some PEL type Shimura varieties.

Keywords: -divisible groups, Shimura varieties

Class. math. : 14K02,14K10,14L05,11F33

ISSN : 0012-9593
Publié avec le concours de : Centre National de la Recherche Scientifique

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