On the global structure of special cycles on unitary Shimura varieties
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Publication:2871245
DOI10.4153/CJM-2013-004-1zbMATH Open1325.14041arXiv1110.0863OpenAlexW3101146863MaRDI QIDQ2871245
Publication date: 22 January 2014
Published in: Canadian Journal of Mathematics (Search for Journal in Brave)
Abstract: In this paper, we study the reduced loci of special cycles on local models of the Shimura variety for GU(1; n-1). We explicitly compute the global structure of the reduced locus of a single special cycle, as well as of an arbitrary intersection of special cycles, 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.
Full work available at URL: https://arxiv.org/abs/1110.0863
Related Items (7)
Cones of special cycles of codimension 2 on orthogonal Shimura varieties ⋮ Tate cycles on some unitary Shimura varieties mod \(p\) ⋮ Vertical Distribution Relations for Special Cycles on Unitary Shimura Varieties ⋮ Unitary cycles on Shimura curves and the Shimura lift. I ⋮ Special cycles on unitary Shimura varieties. II: Global theory ⋮ Title not available (Why is that?) ⋮ The Modularity of Special Cycles on Orthogonal Shimura Varieties over Totally Real Fields under the Beilinson–Bloch Conjecture
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