WebWe give a proof of the André-Oort conjecture for $\mathcal {A}_g$ — the moduli space of principally polarized abelian varieties. In particular, we show that a recently proven “averaged” version of the Colmez conjecture yields lower bounds for Galois orbits of CM points. The André-Oort conjecture then follows from previous work of Pila and the author. 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 …
[1507.06903v3] On the Averaged Colmez Conjecture
http://faculty.bicmr.pku.edu.cn/~yxy/preprints/averaged_colmez.pdf 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 … crypto token landing page next.js github
The André-Oort conjecture for $\mathcal {A}_g$ - Annals of …
WebColmez’s conjecture has been used by Tsimerman [Ts] to provide an unconditional proof of the Andr e-Ort conjecture for abelian varieties of Hodge type. Around the same time as [AGHMP2] also X. Yuan and S.-W. Zhang [YZ] proved, using di erent techniques, the averaged form of Colmez’s conjecture. 2 The average Colmez conjecture 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 of Artin L-functions. The aim of this paper to prove an averaged version of the conjecture, which was also proposed by Colmez. Publication Date: 2024: Citation: 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 crypto token exchange