Modularity of generating series of divisors on unitary Shimura varieties

Jan Bruinier, Benjamin Howard, Stephen S. Kudla, Michael Rapoport, Tonghai Yang

Published 2017-02-25Version 1

We form generating series of special divisors, valued in the Chow group and in the arithmetic Chow group, on the compactified integral model of a Shimura variety associated to a unitary group of signature (n-1,1), and prove their modularity. The main ingredient of the proof is the calculation of the vertical components appearing in the divisor of a Borcherds product on the integral model.