Faltings heights of abelian varieties with complex multiplication

By F. Andreatta, Eyal Z. Goren, Benjamin Howard, Keerthi Madapusi Pera. 2015

62 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a19ef706e97ddf7c398266821777325033a26da0

Citations in the corpus

• Applications of the hyperbolic Ax–Schanuel conjecture (2017, unknown): “This hypothesis, which was verified by Tsimerman for special points of A g [30] via progress on the Colmez conjecture due to Andreatta, Goren, Howard, Madapusi Pera, Yuan, and Zhang [1, 40], is now the only obstacle in an otherwise unconditional proof of the André-Oort conjecture.”