A guide to the reduction modulo p of Shimura varieties

Details A guide to the reduction modulo p of Shimura varieties A guide to the reduction modulo p of Shimura varieties

2002-05-02

arxiv.org/abs/math/0205022v1

Mathematics

Algebraic Geometry

AMS-TeX, 40 pages

Scientific paper

This is a report on results and methods in the reduction modulo p of Shimura varieties with parahoric level structure. In the first part, the local theory, we explain the concepts of parahoric subgroups, of the mu-admissible and mu-permissible subsets of the Iwahori-Weyl group, of the corresponding union of affine Deligne-Lusztig varieties and of local models. In the second part, the global theory, we use these concepts to formulate conjectures on the points in the reduction modulo p of Shimura varieties with parahoric level structure.

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