Stratifications in the reduction of Shimura varieties

By Xuhua He, Michael Rapoport. 2015

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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.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/144d8e5e8f991e9ceccde20ce19b7da97df10c26