# Modularity of generating series of divisors on unitary Shimura varieties

@article{Bruinier2020ModularityOG,
title={Modularity of generating series of divisors on unitary Shimura varieties},
author={Jan H. Bruinier and Benjamin J. Howard and Stephen S. Kudla and Michael Rapoport and Tonghai Yang},
journal={Ast{\'e}risque},
year={2020}
}
• Published 25 February 2017
• Mathematics
• Astérisque
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.
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