Eva Viehmann

Ekedahl–Oort and Newton strata for Shimura varieties of PEL type

We study the Ekedahl–Oort stratification for good reductions of Shimura varieties of PEL type. These generalize the Ekedahl–Oort strata defined and studied by Oort for the moduli space of principally polarized abelian varieties (the “Siegel case”). They are parameterized by certain elements

Moduli spaces of -divisible groups

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Foliations in deformation spaces of local G-shtukas

in the Weyl group of the reductive group of the Shimura datum. We show that for every such

Generalized affine Springer fibres

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Truncations of level 1 of elements in the loop group of a reductive group

the corresponding Ekedahl–Oort stratum is smooth, quasi-affine, and of dimension