Ekedahl-Oort strata and Kottwitz-Rapoport strata

JOURNAL OF ALGEBRA

卷:351

Article

Goertz, Ulrich¹  Hoeve, Maarten² 

[1] Univ Duisburg Essen, Inst Expt Math, D-45326 Essen, Germany

[2] Univ Amsterdam, Korteweg de Vries Inst, NL-1018 TV Amsterdam, Netherlands

关键词: Moduli spaces of abelian varieties in positive characteristic;    Reduction of Siegel modular varieties;    Ekedahl-Oort stratification;    Kottwitz-Rapoport stratification;   

DOI  :  10.1016/j.jalgebra.2011.10.039

来源: Elsevier

【 摘 要 】

We study Ekedahl-Oort strata on the moduli space A(g) of g-dimensional principally polarized abelian varieties in positive characteristic, and Kottwitz-Rapoport strata on its variants A(j) with parahoric level structure. First, we show that every Ekedahl-Oort stratum is isomorphic to a parahoric Kottwitz-Rapoport stratum. Second, both supersingular Ekedahl-Oort strata and supersingular Kottwitz-Rapoport strata are isomorphic to disjoint unions of Deligne-Lusztig varieties (see Hoeve (2010) [10] and Gortz and Yu (2010) [5] resp.), and here we compare these isomorphisms. Finally we give an explicit description of Kottwitz-Rapoport strata contained in the supersingular locus in the general parahoric case. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free