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Ekedahl-Oort Strata for Good Reductions of Shimura Varieties of Hodge Type

Published online by Cambridge University Press:  20 November 2018

Chao Zhang
Chao Zhang*
Affiliation:
Yau Mathematical Sciences Center, Tsinghua University, Beijing, China e-mail: zhangchao1217@gmail.com
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Abstract

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For a Shimura variety of Hodge type with hyperspecial level structure at a prime $p$, Vasiu and Kisin constructed a smooth integral model (namely the integral canonical model) uniquely determined by a certain extension property. We define and study the Ekedahl-Oort stratifications on the special fibers of those integral canonical models when $p\,>\,2$. This generalizes Ekedahl-Oort stratifications defined and studied by Oort on moduli spaces of principally polarized abelian varieties and those defined and studied by Moonen, Wedhorn, and Viehmann on good reductions of Shimura varieties of PEL type. We show that the Ekedahl-Oort strata are parameterized by certain elements $w$ in the Weyl group of the reductive group in the Shimura datum. We prove that the stratum corresponding to $w$ is smooth of dimension $l\left( w \right)$ (i.e., the length of $w$) if it is non-empty. We also determine the closure of each stratum.

Keywords

14G3511G18Shimura varietyF-zip
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 70 , Issue 2 , 01 April 2018 , pp. 451 - 480
Copyright
Copyright © Canadian Mathematical Society 2018

References

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