Adapted deformations and Ekedahl-Oort stratifications of Shimura varieties

The thesis deals with the Ekedahl-Oort stratification of the special fibre of Shimura varieties of Hodge type. We construct a morphism of schemes from a(n) (fppf-)torsor of the special fibre of Shimura variety to a subquotient scheme of the loop group of the associated reductive group of the Shimura varieties. This morphism is given roughly given by the Frobenii of a family of p-divisible groups associated to the Shimura variety. We show that this morphism induces a morphism of fpqc sheaves from the Shimura variety in question to an fpqc subquotient sheaf of the loop group. We show in the end that the geometric fibre of this morphism give back the Ekedahl-Oort strata of the Shimura variety: this gives a conceptual interpretation of Eva Viehmann's new invariants of truncation of level 1 of loop groups.