Arithmetic theta series

Abstract: In recent joint work with Jan Bruinier, Ben Howard, Michael Rapoport and Tonghai Yang, we proved that a certain generating series for the classes of arithmetic divisors on a regular integral model M of a Shimura variety for a unitary group of signature (n-1,1) for an imaginary quadratic field is a modular form of weight n valued in the first arithmetic Chow group of M. I will discuss how this is proved, highlighting the main steps. Key ingredients include information about the divisors of Borcherds forms on the integral model and the behavior of Green functions at the boundary.