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On the Global Structure of Special Cycles on Unitary Shimura Varieties

Published online by Cambridge University Press:  20 November 2018

Nicolas Vandenbergen
Nicolas Vandenbergen*
Affiliation:
Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany, e-mail: nvdb@math.uni-bonn.de
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Abstract

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In this paper, we study the reduced loci of special cycles on local models of the Shimura variety for $\text{GU}\left( 1,\,n\,-\,1 \right)$. 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

14G35Shimura varietieslocal modelsspecial cycles
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 65 , Issue 5 , 01 October 2013 , pp. 1125 - 1163
Copyright
Copyright © Canadian Mathematical Society 2013

References

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