Abstract.
In this paper we recall basic properties of complex Shimura varieties and show that they actually characterize them. This characterization immediately implies the explicit form of Kazhdan's theorem on the conjugation of Shimura varieties. It also implies the existence of unique equivariant models over the reflex field of Shimura varieties corresponding to adjoint groups and the existence of a p-adic uniformization of certain unitary Shimura varieties. In the appendix we give a modern formulation and a proof of Weil's descent theorem.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Varshavsky, Y. On the characterization of complex Shimura varieties. Sel. math., New ser. 8, 283–314 (2002). https://doi.org/10.1007/s00029-002-8107-1
Issue Date:
DOI: https://doi.org/10.1007/s00029-002-8107-1