On the characterization of complex Shimura varieties

Y. Varshavsky ^[1]
1. [1] University of Toronto
  
  University of Toronto
  
  Canadá
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 8, Nº. 2, 2002, págs. 283-314
Idioma: inglés
Enlaces
- Texto completo (pdf)
Resumen
- 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.