Web24 de jul. de 2015 · 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. Weba recently proven \averaged" version of the Colmez conjecture yields lower bounds for Galois orbits of CM points. The Andr e-Oort conjecture then follows from previous work of Pila and the author. 1. Introduction Recall the statement of the Andr e-Oort conjecture: Conjecture 1.1. Let Sbe a Shimura variety, and let V be an irreducible

The André-Oort conjecture for $\mathcal {A}_g$ - Annals of …

Web1 de nov. de 2024 · 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 … WebThe 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 … candyologist position

Faltings heights and Zariski density of CM abelian varieties

WebUsing this, the averaged Colmez conjecture for E can be reduced to the exact Colmez conjecture for (E♯,Φ♯). Admittedly, at the moment this looks less like a reduction and … http://faculty.bicmr.pku.edu.cn/~yxy/preprints/averaged_colmez.pdf WebWhen d=2, Yang [Yan13] was able to prove Colmez’s conjecture in many cases, including the rst known cases of non-abelian extensions. Our rst main result, stated in the text as Theorem 9.5.5, is the proof of an averaged form of Colmez’s conjecture for a xed E, obtained by averaging both sides of the conjectural formula over all CM types. candy omori