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Les chtoucas locaux sont des analogues en égales caractéristiques des groupes -divisibles — par exemple on leur associe un module de Tate, qui est un module libre sur l’anneau d’entiers d’un corps local de caractéristique positive. Nous associons à un chtouca local une structure de Hodge (ou, plus précisément, une structure de Hodge-Pink), ce qui induit un morphisme de périodes analogue à celui construit par Rapoport et Zink. Pour les structures de Hodge-Pink définies sur une extension finie...
On étudie la relation entre le -rang des variétés abéliennes en caractéristique et
la stratification de Kottwitz-Rapoport de la fibre spéciale en de l’espace de module
des variétés abéliennes principalement polarisées avec structure de niveau de type
Iwahori en . En particulier, on démontre la densité du lieu ordinaire dans cette fibre
spéciale.
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