Ekedahl-Oort Strata for Good Reductions of Shimura Varieties of Hodge Type
By Chao Zhang. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2013
51 citations recorded by the source corpus.
Abstract 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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/08756c16940a628b787268c001f9b5fbd1069d5d
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Strata Hasse invariants, Hecke algebras and Galois representations (2015, background): “n in the Siegel and PEL cases respectively. In his thesis, Zhang constructed a universal G-zip over the special fiber of a general Hodge-type Shimura variety. He proved that the induced map ζis smooth [113] (see also [110]). I.1.2. Hasse invariants. The theory of Hasse invariants in its modern form g”