Abstract
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.
Authors
Fabrizio Andreatta
Dipartimento di Matematica ``Federigo Enriques", Università di Milano,\hfill\break\indent Milano, Italia
Eyal Z. Goren
Department of Mathematics and Statistics, McGill University,\hfill\break\indent 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