Current Developments in Mathematics

Volume 2018

On the averaged Colmez conjecture

Pages: 125 – 178



Benjamin Howard (Boston College, Chestnut Hill, Massachusetts, U.S.A.)


This is an expository article on the averaged version of Colmez’s conjecture, relating Faltings heights of CM abelian varieties to Artin $L$-functions. It is based on the author’s lectures at the Current Developments in Mathematics conference held at Harvard in 2018.

This research was supported in part by NSF grants DMS-1201480 and DMS-1501583.

Published 17 December 2019