@article{62245480d21f415e908ccbe2a318e77c,
title = "On the averaged Colmez conjecture",
abstract = "The Colmez conjecture is a formula expressing the Faltings height of an abelian variety with complex multiplication 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, which was also proposed by Colmez.",
keywords = "Arithmetic intersection, Colmez conjecture, Complex multiplication, Faltings height, L-function, Shimura curve",
author = "Xinyi Yuan and Zhang, {Shou Wu}",
note = "Funding Information: The authors would like to thank Pierre Colmez, Yichao Tian, Tonghai Yang, and Wei Zhang for helpful discussions. XY would like to thank the hospitality of AMSS of Chinese Academy of Sciences and acknowledge the support of the National Science Foundation under the award DMS-1330987. SZ would like to thank the AMSS of Chinese Academy of Sciences and the IAS of Tsinghua University for their hospitality during the preparation of this work, and the National Science Foundation for its support via awards DMS-1415502 and DMS-1404369. Publisher Copyright: {\textcopyright} 2018 Department of Mathematics, Princeton University.",
year = "2018",
month = mar,
day = "1",
doi = "10.4007/annals.2018.187.2.4",
language = "English (US)",
volume = "187",
pages = "533--638",
journal = "Annals of Mathematics",
issn = "0003-486X",
publisher = "Princeton University Press",
number = "2",
}