Stratifications in the reduction of Shimura varieties

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.

19 pages

References in corpus (7)

• A guide to the reduction modulo p of Shimura varieties
• Towards a theory of local Shimura varieties
• Introduction to Shimura varieties with bad reduction of parahoric type
• On parahoric subgroups
• Minimal length elements in conjugacy classes of extended affine Weyl group
• Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties
• Vertexwise criteria for admissibility of alcoves

Cited by in corpus (1)

• Hecke algebras and $p$-adic groups