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Stratifications in the reduction of Shimura varieties

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Abstract

In the paper four stratifications in the reduction modulo p of a general Shimura variety are studied: the Newton stratification, the Kottwitz–Rapoport stratification, the Ekedahl–Oort stratification and the Ekedahl–Kottwitz–Oort–Rapoport stratification. We formulate a system of axioms and show that these imply non-emptiness statements and closure relation statements concerning these various stratifications. These axioms are satisfied in the Siegel case.

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Authors and Affiliations

  1. Department of Mathematics, University of Maryland, College Park, MD, 20742-4015, USA

    X. He

  2. Department of Mathematics, HKUST, New Territories, Hong Kong, China

    X. He

  3. Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    M. Rapoport

Authors
  1. X. He
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  2. M. Rapoport
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Correspondence to X. He.

Additional information

X. H. was partially supported by NSF DMS-1463852. M.R. was supported by the Deutsche Forschungsgemeinschaft through the Grant SFB/TR 45.

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He, X., Rapoport, M. Stratifications in the reduction of Shimura varieties. manuscripta math. 152, 317–343 (2017). https://doi.org/10.1007/s00229-016-0863-x

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  • DOI: https://doi.org/10.1007/s00229-016-0863-x

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