1999/09/23 by Yakov Varshavsky, Varshavsky, Yakov · 1 citation
Mathematics · #11G18 #14G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G18 #msc:14G35
paper · pdf · doi:10.48550/arxiv.math/9909142
31 pages
arxiv created 1999/09/23 · openalex publication_date 1999/09/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we recall the construction and basic properties of complex Shimura varieties and show that these properties actually characterize them. This characterization immediately implies the explicit form of Kazhdan's theorem on the conjugation of Shimura varieties. As a further corollary, we show that each Shimura variety corresponding to an adjoint group has a canonical model over its reflex field. We also indicate how this characterization implies the existence of a p-adic uniformization of certain unitary Shimura varieties. In the appendix we give a complete scheme-theoretic proof of Weil's descent theorem.