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Local models of Shimura varieties, I. Geometry and combinatorics

G. Pappas, M. Rapoport, B. Smithling

Number 24
Author Michael Rapoport
Project B07
Year 2010

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.

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