Kottwitz-Rapoport and p-rank strata in the reduction of Shimura varieties of PEL type

2012/10/04 by Philipp Hartwig, Hartwig, Philipp
Mathematics · #14G35 #14K10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1210.1559

openalex publication_date 2012/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the reduction of certain integral models of Shimura varieties of PEL type with Iwahori level structure. On these spaces we have the Kottwitz-Rapoport and the p-rank stratification. We show that the p-rank is constant on a KR stratum, generalizing a result of Ngô and Genestier. We prove an abstract, uniform formula for the p-rank on a KR stratum. In the symplectic and in the unitary case we derive explicit formulas for its value. We apply these formulas to the question of the density of the ordinary locus and to the question of the dimension of the p-rank 0 locus.

Citations

• Introduction to Shimura varieties with bad reduction of parahoric type
• Local models of Shimura varieties and a conjecture of Kottwitz

Related

• Stratifications in the reduction of Shimura varieties
• EKOR strata on Shimura varieties with parahoric reduction
• Ekedahl-Oort strata for good reductions of Shimura varieties of Hodge type
• Stratifications and foliations for good reductions of Shimura varieties of Hodge type
• On the geometry of the Pappas-Rapoport models for PEL Shimura varieties