Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications
Number Theory
2020-02-25 v2 Algebraic Geometry
Abstract
We prove two formulas in the style of the Gross-Zagier theorem, relating derivatives of L-functions to arithmetic intersection pairings on a unitary Shimura variety. We also prove a special case of Colmez's conjecture on the Faltings heights of abelian varieties with complex multiplication. These results are derived from the authors' earlier results on the modularity of generating series of divisors on unitary Shimura varieties.
Keywords
Cite
@article{arxiv.1710.00628,
title = {Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications},
author = {Jan Bruinier and Benjamin Howard and Stephen S. Kudla and Michael Rapoport and Tonghai Yang},
journal= {arXiv preprint arXiv:1710.00628},
year = {2020}
}
Comments
Final version. To appear in Asterisque