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

@article{Viehmann2010EkedahlOortAN,
  title={Ekedahl–Oort and Newton strata for Shimura varieties of PEL type},
  author={Eva Viehmann and Torsten Wedhorn},
  journal={Mathematische Annalen},
  year={2010},
  volume={356},
  pages={1493-1550}
}
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 $$w$$ in the Weyl group of the reductive group of the Shimura datum. We show that for every such $$w$$ the corresponding Ekedahl–Oort stratum is smooth, quasi-affine, and of dimension $$\ell (w)$$ (and in… 
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