Ekedahl-Oort strata and the first Newton slope strata

Ekedahl-oort Strata in the Supersingular Locus

We give a description of the individual Ekedahl-Oort strata contained in the supersingular locus in terms of Deligne-Lusztig varieties, refining a result of Harashita.

Ekedahl - Oort strata contained in the supersingular locus

In this paper we show that, for each Ekedahl-Oort stratum contained in the supersingular locus, the number of its irreducible components is equal to a class number of a quaternion unitary group. MSC: primary: 14K10; secondary: 11G10; 14L05

Newton Polygon Strata in the Moduli Space of Abelian Varieties

Newton Strata in the Loop Group of a Reductive Group

We generalize purity of the Newton stratification to purity for a single break point of the Newton point in the context of local G-shtukas respectively of elements of the loop group of a reductive group. As an application we prove that elements of the loop group bounded by a given dominant coweight satisfy a generalization of Grothendieck’s conjecture on deformations of p-divisible groups with ...

Truncations of Level 1 of Elements in the Loop Group of a Reductive Group

We generalize the notion of Ekedahl-Oort strata to elements in the loop group of any connected reductive group, and call the resulting discrete invariant the truncation of level 1 of the element. We give conditions for the Newton points occurring among the elements of a given truncation of level 1 and especially for the generic Newton point in a given truncation stratum. We prove that truncatio...