A guide to the reduction modulo p of Shimura varieties
arXiv:math/0205022
Abstract
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.
AMS-TeX, 40 pages
Cited by in corpus (7)
- Introduction to Shimura varieties with bad reduction of parahoric type
- On the Hodge-Newton decomposition for split groups
- Dimensions of some affine Deligne-Lusztig varieties
- On the slope stratification of certain Shimura varieties
- Formulas for the dimensions of some affine Deligne-Lusztig Varieties
- Existence de F-cristaux avec structures supplementaires
- A converse to Mazur's inequality for split classical groups