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Stratifications in the reduction of Shimura varieties. (English) Zbl 1432.14023
Summary: 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.

MSC:
14G35 Modular and Shimura varieties
14M15 Grassmannians, Schubert varieties, flag manifolds
20G25 Linear algebraic groups over local fields and their integers
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