On the characterization of complex Shimura varieties

Yakov Varshavsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageAmerican English
Pages (from-to)283-314
Number of pages32
JournalSelecta Mathematica, New Series
Issue number2
StatePublished - 2002

Bibliographical note

Funding Information:
This work was mainly conceived while the author enjoyed the hospitality and the financial support of the Max-Planck-Institute für Mathematik in Bonn.


  • Shimura varieties
  • Weil descent


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