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On the Global Structure of Special Cycles on Unitary Shimura Varieties

Published:2013-07-16
Printed: Oct 2013
• Nicolas Vandenbergen,
Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
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Abstract

In this paper, we study the reduced loci of special cycles on local models of the Shimura variety for $\operatorname{GU}(1,n-1)$. Those special cycles are defined by Kudla and Rapoport. We explicitly compute the irreducible components of the reduced locus of a single special cycle, as well as of an arbitrary intersection of special cycles, and their intersection behaviour in terms of Bruhat-Tits theory. Furthermore, as an application of our results, we prove the connectedness of arbitrary intersections of special cycles, as conjectured by Kudla and Rapoport.
 Keywords: Shimura varieties, local models, special cycles
 MSC Classifications: 14G35 - Modular and Shimura varieties [See also 11F41, 11F46, 11G18]

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