English

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