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arXiv · 1404.0577

Purity of Zip Strata with Applications to Ekedahl-Oort Strata of Shimura Varieties of Hodge Type

Torsten Wedhorn·Yaroslav Yatsyshyn
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Abstract

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.

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Torsten Wedhorn, Yaroslav Yatsyshyn. 2014-04-02. Purity of Zip Strata with Applications to Ekedahl-Oort Strata of Shimura Varieties of Hodge Type. https://arxiv.org/abs/1404.0577

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