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.

Authors

Xinyi Yuan

Department of Mathematics, University of California, Berkeley, CA 94720

Shou-Wu Zhang

Department of Mathematics, Princeton University, Princeton, NJ 08544