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.
Citation
Fabrizio Andreatta. Eyal Goren. Benjamin Howard. Keerthi Madapusi Pera. "Faltings heights of abelian varieties with complex multiplication." Ann. of Math. (2) 187 (2) 391 - 531, March 2018. https://doi.org/10.4007/annals.2018.187.2.3
Information
