The \mu-ordinary locus for Shimura varieties of Hodge type

By Daniel Wortmann. 2013

49 citations recorded by the source corpus.

We review the Newton stratification and Ekedahl-Oort stratification on the special fiber of a smooth integral model for a Shimura variety of Hodge type at a prime of good reduction. We show that the \mu-ordinary locus coincides with the generic Ekedahl-Oort stratum, and that for any two geometric points in the \mu-ordinary locus there is an isomorphism of the attached Dieudonne modules with additional structure. As a consequence, we proof that the \mu-ordinary locus is open and dense, thus generalizing the results which were already known in the PEL-case. To prove our results we provide a method which allows to reduce the equality of strata to a group theoretic statement.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/df9e8a0cb2abf29c3938d7e2bb6a3b4253899fd4

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In Geometry and Topology

1. Paul Ziegler
2. R. Pink
3. T. Wedhorn
4. Chao Zhang
5. Jonathan Pila
6. Xuhua He
7. E. Lau
8. Ehud Hrushovski

In Mathematical Physics

1. Paul Ziegler
2. R. Pink
3. T. Wedhorn
4. Chao Zhang
5. Xuhua He
6. E. Lau

Citations in the corpus

• $F$-zips with additional structure (2012, background): “Wortmann in [25] to prove that the conjectured candidate for the generic Newton stratum is indeed open and dense in the special fiber.”