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p-adic uniformization of unitary Shimura varieties

Yakov Varshavsky
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Abstract

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.

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Yakov Varshavsky. 1999-09-23. p-adic uniformization of unitary Shimura varieties. https://arxiv.org/abs/math/9909143

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