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arXiv · 1508.00178

Faltings heights of abelian varieties with complex multiplication

Fabrizio Andreatta·Eyal Z. Goren·Benjamin Howard·Keerthi Madapusi Pera
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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 $L$-functions. As an application of this result, we prove an averaged version of Colmez's conjecture on the Faltings heights of CM abelian varieties.

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Fabrizio Andreatta, Eyal Z. Goren, Benjamin Howard, Keerthi Madapusi Pera. 2017-09-30. Faltings heights of abelian varieties with complex multiplication. https://arxiv.org/abs/1508.00178

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