On the characterization of complex Shimura varieties

Yakov Varshavsky

doi:10.1007/s00029-002-8107-1

On the characterization of complex Shimura varieties

Yakov Varshavsky^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English
Pages (from-to)	283-314
Number of pages	32
Journal	Selecta Mathematica, New Series
Volume	8
Issue number	2
DOIs	https://doi.org/10.1007/s00029-002-8107-1
State	Published - 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.

Keywords

Shimura varieties
Weil descent

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10.1007/s00029-002-8107-1

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On the characterization of complex Shimura varieties

Abstract

Bibliographical note

Keywords

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