On the Averaged Colmez Conjecture

TL;DR

This paper proves an averaged version of the Colmez conjecture, linking the Faltings height of CM abelian varieties to derivatives of Artin L-functions, advancing understanding in number theory.

Contribution

It introduces a proof of an averaged form of the Colmez conjecture, a significant step in understanding heights of CM abelian varieties.

Findings

Proved the averaged Colmez conjecture.

Connected Faltings heights with Artin L-function derivatives.

Enhanced understanding of CM abelian varieties.

Abstract

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.