English

Faltings heights of abelian varieties with complex multiplication

Number Theory 2017-10-03 v3

Abstract

Let M be the Shimura variety associated with the group of spinor similitudes of a rational quadratic space over of signature (n,2). We prove a conjecture of Bruinier-Kudla-Yang, relating the arithmetic intersection multiplicities of special divisors and big CM points on M to the central derivatives of certain LL-functions. As an application of this result, we prove an averaged version of Colmez's conjecture on the Faltings heights of CM abelian varieties.

Keywords

Cite

@article{arxiv.1508.00178,
  title  = {Faltings heights of abelian varieties with complex multiplication},
  author = {Fabrizio Andreatta and Eyal Z. Goren and Benjamin Howard and Keerthi Madapusi Pera},
  journal= {arXiv preprint arXiv:1508.00178},
  year   = {2017}
}

Comments

Final version. To appear in Annals of Math