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

Zhang, Chao

Canadian journal of mathematics, Tome 70 (2018) no. 2, pp. 451-480

Résumé

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) uniquelydetermined by a certain extension property. We define and study the Ekedahl-Oort stratificationson 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 abelianvarieties 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.

Détail

DOI : 10.4153/CJM-2017-020-5

Mots-clés : 14G35, 11G18, Shimura variety, F-zip

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