1999/09/23 by Yakov Varshavsky
Mathematics · #math.NT #math.AG #msc:14G35 #msc:11G18
published as Inst. Hautes Etudes Sci. Publ. Math. No. 87 (1998) 57-119 · 67 pages
arxiv created 1999/09/23 · arxiv updated 2009/11/30
In this paper we generalize Cherednik's method and prove that certain Shimura varieties corresponding to groups of unitary similitudes and automorphic vector bundles over them have p-adic uniformization. This is proved for Shimura varieties, uniformized by the complex unit ball, when the central simple algebra over a CM-field defining the group of unitary similitudes has Brauer invariant 1/d at p. In this case, Shimura varieties can be uniformized by Drinfeld's covers of p-adic upper half-spaces.