Local models of Shimura varieties, I. Geometry and combinatorics

2010/11/25 by Pappas, G., Rapoport, M., Smithling, B. · 4 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1011.5551

Abstract

We survey the theory of local models of Shimura varieties. In particular, we discuss their definition and illustrate it by examples. We give an overview of the results on their geometry and combinatorics obtained in the last 15 years. We also exhibit their connections to other classes of algebraic varieties such as nilpotent orbit closures, affine Schubert varieties, quiver Grassmannians and wonderful completions of symmetric spaces.

Cited by

• Topological flatness of orthogonal spin local models
• Equivariant cohomology of juggling varieties in rank one
• Dual Shellability of Admissible Set and Cohen-Macaulayness of Local Models
• Global positroid varieties

Related

• Local models of Shimura varieties and a conjecture of Kottwitz
• Shimura varieties
• Towards a theory of local Shimura varieties
• Local models, Mustafin varieties and semi-stable resolutions
• Generalized juggling patterns, quiver Grassmannians and affine flag varieties