Introduction to Shimura varieties with bad reduction of parahoric type

2004/09/24 by Thomas J. Haines, Haines, Thomas J. · 9 citations
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paper · pdf · doi:10.48550/arxiv.math/0409482

An expanded version of my short course in the June 2003 Summer School on Harmonic Analysis, the Trace Formula, and Shimura Varieties, held at the Fields Institute; 63 pp., 2 figures

arxiv created 2004/09/24 · openalex publication_date 2004/09/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This survey article explains the construction of Rapoport-Zink local models and their use in understanding various questions relating to the singularities in the reduction modulo p of certain Shimura varieties with parahoric level structure at p.

Citations

• A guide to the reduction modulo p of Shimura varieties

Cited by

• Trace of Frobenius on nearby cycles for a Γ₁(p)-local model
• On the geometry of integral models of Shimura varieties with Γ₁(p)-level structure
• Dual Shellability of Admissible Set and Cohen-Macaulayness of Local Models
• Central leaves on Shimura varieties with parahoric reduction
• EKOR strata for Shimura varieties with parahoric level structure
• Notes on partial conjugation
• Torsion in the Coherent Cohomology of Shimura Varieties and Galois Representations
• Kottwitz-Rapoport and p-rank strata in the reduction of Shimura varieties of PEL type
• On the reduction of the Siegel moduli space of abelian varieties of dimension 3 with Iwahori level structure

Related

• A guide to the reduction modulo p of Shimura varieties
• Integral models of Shimura varieties with parahoric level structure, II
• Local models in the ramified case. II. Splitting models
• On the flatness of local models for the symplectic group
• EKOR strata for Shimura varieties with parahoric level structure