Faltings heights of abelian varieties with complex multiplication


Let $M$ be the Shimura variety associated with the group of spinor similitudes of a quadratic space over $\mathbb {Q}$ 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 $L$-functions.

As an application of this result, we prove an averaged version of Colmez’s conjecture on the Faltings heights of CM abelian varieties.


Fabrizio Andreatta

Dipartimento di Matematica ``Federigo Enriques", Università di Milano, Milano, Italia

Eyal Z. Goren

Department of Mathematics and Statistics, McGill University, Montreal, QC, Canada

Benjamin Howard

Department of Mathematics, Boston College, Chestnut Hill, MA

Keerthi Madapusi Pera

Department of Mathematics, University of Chicago, Chicago, IL

Current address:

Department of Mathematics, Boston College,\hfill\break\indent Chestnut Hill, MA