EKOR strata on Shimura varieties with parahoric reduction

2020/03/06 by Jens Hesse, Hesse, Jens
Mathematics · Physics and Astronomy · #14D23 #14F40 (Secondary) #14G35 (Primary) 11G18 #14L05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2003.04738

openalex publication_date 2020/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the geometry of the special fiber of the integral model of a Shimura variety with parahoric level at a given prime place. To be more precise, we deal with the EKOR stratification which interpolates between the Ekedahl-Oort and Kottwitz-Rapoport stratifications. In the Siegel case we give a geometric description by suitably generalizing the theory of G-zips of Moonen, Wedhorn, Pink and Ziegler to our context.

Citations

• A guide to the reduction modulo p of Shimura varieties
• The μ-ordinary locus for Shimura varieties of Hodge type

Related

• EKOR strata for Shimura varieties with parahoric level structure
• Compactifications of subschemes of integral models of Hodge-type Shimura Varieties with Parahoric level structures
• Ekedahl-Oort strata for good reductions of Shimura varieties of Hodge type
• Central leaves on Shimura varieties with parahoric reduction
• Integral models of Shimura varieties with parahoric level structure