On the Averaged Colmez Conjecture
Xinyi Yuan, Shou-Wu Zhang

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.
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