Introduction to Shimura varieties with bad reduction of parahoric type

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.

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

References in corpus (6)

• A guide to the reduction modulo p of Shimura varieties
• Iwahori-Hecke Algebras
• The local Langlands correspondence for GL(n) over p-adic fields
• Alcoves et p-rang des variétés abéliennes
• The Jordan-Hoelder series for nearby cycles on some Shimura varieties and affine flag varieties
• Topological flatness of local models in the ramified case

Cited by in corpus (14)

• Torsion in the Coherent Cohomology of Shimura Varieties and Galois Representations
• p-adic Hodge-theoretic properties of étale cohomology with mod p coefficients, and the cohomology of Shimura varieties
• Mod-$p$ isogeny classes on Shimura varieties with parahoric level structure
• EKOR strata for Shimura varieties with parahoric level structure
• Hecke algebras and $p$-adic groups
• Closure of Steinberg fibers and affine Deligne-Lusztig varieties
• On the reduction of the Siegel moduli space of abelian varieties of dimension 3 with Iwahori level structure
• Central leaves on Shimura varieties with parahoric reduction
• Good and semi-stable reductions of Shimura varieties
• Stratifications in the reduction of Shimura varieties
• Convex Polytopes for the Central Degeneration of the Affine Grassmannian
• EKOR strata on Shimura varieties with parahoric reduction
• Notes on partial conjugation
• Kottwitz-Rapoport and p-rank strata in the reduction of Shimura varieties of PEL type