%0 Journal Article
%T Purity of Zip Strata with Applications to Ekedahl-Oort Strata of Shimura Varieties of Hodge Type
%A Torsten Wedhorn
%A Yaroslav Yatsyshyn
%J Mathematics
%D 2014
%I arXiv
%X We show that the zip stratification given by an arbitrary $\Ghat$-zip over a scheme is pure. We deduce purity of the level-$m$-stratification for truncated Barsotti-Tate groups and purity of the Ekedahl-Oort stratification for special fibers of good models of Shimura varieties of Hodge type. We also show that all Ekedahl-Oort strata are quasi-affine schemes and generalize several properties of the Bruhat stratification from the PEL case to the case of Shimura varieties of Hodge type.
%U http://arxiv.org/abs/1404.0577v1