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.

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Authors

Xinyi Yuan

University of California at Berkeley, Berkeley, CA

Shou-Wu Zhang

Princeton University, Princeton, NJ