Stratifications and foliations for good reductions of Shimura varieties of Hodge type

Abstract

Level $m$-stratifications on PEL Shimura varieties are defined and studied by Wedhorn using BT-$m$s with PEL structure, and then by Vasiu for general Hodge type Shimura varieties using Shimura $F$-crystals. The theory of foliations is established by Oort for Siegel modular varieties, and by Mantovan for PEL Shimura varieties. It plays an important role in Hamacher's work to compute the dimension of Newton strata of PEL Shimura varieties. We study level $m$ stratifications on good reductions at $p>2$ of Shimura varieties of Hodge type by constructing certain torsors together with equivariant morphisms, and relating them to truncated displays. We then use the results obtained to extend the theory of foliations to these reductions. As a consequence, combined with results of Nie and Zhu, we get a dimension formula for Newton strata.

first draft, 40 pages

References in corpus (10)

• Ekedahl-Oort and Newton strata for Shimura varieties of PEL type
• Rapoport-Zink spaces for spinor groups
• $F$-zips with additional structure
• Crystalline boundedness principle
• The μ-ordinary locus for Shimura varieties of Hodge type
• Manin problems for Shimura varieties of Hodge type
• Affine Grassmannians and the geometric Satake in mixed characteristic
• Purity of Zip Strata with Applications to Ekedahl-Oort Strata of Shimura Varieties of Hodge Type
• Fundamental elements of an affine Weyl group
• Remarks on Ekedahl-Oort stratifications

Cited by in corpus (5)

• Rapoport-Zink spaces for spinor groups
• On the Newton stratification in the good reduction of Shimura varieties
• Eichler-Shimura Relations for Shimura Varieties of Hodge Type
• Hecke eigensystems of automorphic forms (mod $p$) of Hodge type and algebraic modular forms
• EKOR strata on Shimura varieties with parahoric reduction