Modularity of generating series of divisors on unitary Shimura varieties
Number Theory
2020-02-25 v3 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1702.07812,
title = {Modularity of generating series of divisors on unitary Shimura varieties},
author = {Jan Bruinier and Benjamin Howard and Stephen S. Kudla and Michael Rapoport and Tonghai Yang},
journal= {arXiv preprint arXiv:1702.07812},
year = {2020}
}
Comments
Final version. To appear in Asterisque