On the Averaged Colmez Conjecture

By Xinyi Yuan, Shou-wu Zhang. 2015

57 citations recorded by the source corpus.

The Colmez conjecture, proposed by Colmez, is a conjecture expressing the Faltings height of a CM abelian variety in terms of some linear combination of logarithmic derivatives of Artin L-functions. The aim of this paper to prove an averaged version of the conjecture.

Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1135679f90780d7e012d0b8d5ad383f001a2ef2a

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.”
• Faltings heights of abelian varieties with complex multiplication (2015, unknown): “on the left is over all CM types of E, and DE and DF are the discriminants of Eand F, respectively. Remark 1.1.1. Very shortly after this theorem was announced, Yuan-Zhang also announced a proof; see [YZ15]. The proofs are very different. The proof of Yuan-Zhang is based on the Gross-Zagier style res”