English

On the global structure of special cycles on unitary Shimura varieties

Algebraic Geometry 2019-08-15 v1 Number Theory

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.

Keywords

Cite

@article{arxiv.1110.0863,
  title  = {On the global structure of special cycles on unitary Shimura varieties},
  author = {Nicolas Vandenbergen},
  journal= {arXiv preprint arXiv:1110.0863},
  year   = {2019}
}