P-adic uniformization of unitary shimura varieties. II

Yakov Varshavsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

In this paper we show that certain Shimura varieties, uniformized by the product of complex unit balls, can be p-adically uniformized by the product of Drinfeld upper half-spaces and their equivariant coverings. We also extend a p-adic uniformization to automorphic vector bundles. It is a continuation of our previous work [38] and contains all cases (up to a central modification) of a uniformization by known p-adic symmetric spaces. The idea of the proof is to show that an arithmetic quotient of the product of Drinfeld upper half-spaces cannot be anything else than a certain unitary Shimura variety. Moreover, we show that difficult theorems of Yau and Kottwitz appearing in [38] may be avoided.

Original languageAmerican English
Pages (from-to)75-113
Number of pages39
JournalJournal of Differential Geometry
Volume49
Issue number1
DOIs
StatePublished - 1998
Externally publishedYes

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