Complex multiplication cycles and Kudla-Rapoport divisors

Abstract

We study the intersections of special cycles on a unitary Shimura variety of signature $(n-1,1)$ and show that the intersection multiplicities of these cycles agree with Fourier coefficients of Eisenstein series. The results are new cases of conjectures of Kudla and suggest a Gross-Zagier theorem for unitary Shimura varieties.

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Authors

Benjamin Howard

Department of Mathematics
Boston College
Chestnut Hill, MA 92467