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Deligne–Lusztig varieties and basic EKOR strata

Part of: Arithmetic problems. Diophantine geometry Arithmetic algebraic geometry

Published online by Cambridge University Press:  29 June 2020

Haining Wang
Haining Wang*
Affiliation:
Department of Mathematics, McGill University, 805 Sherbrooke St W, Montreal, QCH3A 0B9, Canada
*
e-mail: wanghaining1121@outlook.com
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Abstract

Using the axioms of He and Rapoport for the stratifications of Shimura varieties, we explain a result of Görtz, He, and Nie that the EKOR strata contained in the basic loci can be described as a disjoint union of Deligne–Lusztig varieties. In the special case of Siegel modular varieties, we compare their descriptions to that of Görtz and Yu for the supersingular Kottwitz-Rapoport strata and to the descriptions of Harashita and Hoeve for the supersingular Ekedahl–Oort strata.

Keywords

Deligne-Lusztig varietiesShimura varieties

MSC classification

Primary: 14G35: Modular and Shimura varieties
Secondary: 11G18: Arithmetic aspects of modular and Shimura varieties
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 2 , June 2021 , pp. 349 - 367
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Copyright
© Canadian Mathematical Society 2020

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