Adapted deformations and the Ekedahl-Oort stratifications of Shimura varieties

Abstract

This thesis concerns the relation bettween the good

reduction of Shimura varieties and the associated loop groups. To be precise,

by studying the Breuil-Kisin modules of p-divisible groups, we construct a

direct morphism from the special fibre of a Shimura varieties of Hodge type to an fpqc subquotient of the associated loop group, and show that the geometric fibres of the morphism gives back the Ekedahl-Oort strata of the Shimura varieties in question. This can be seen as an alternative definition of the Ekedahl-Oort stratification of Shimura varieties, which gives a conceptual explanation of E. Viehmann's new invariants of "truncation of level 1" of loop groups.