Faltings height and Néron-Tate height of a theta divisor

Abstract

We prove a formula, which, given a principally polarized abelian variety $(A,\lambda )$ over the field of algebraic numbers, relates the stable Faltings height of $A$ with the Néron--Tate height of a symmetric theta divisor on $A$. Our formula completes earlier results due to Bost, Hindry, Autissier and Wagener. The local non-archimedean terms in our formula can be expressed as the tropical moments of the tropicalizations of $(A,\lambda )$.

Final version

References in corpus (3)

• Tropical varieties for non-archimedean analytic spaces
• Non-Archimedean and tropical theta functions
• Néron-Tate heights of cycles on jacobians

Cited by in corpus (2)

• Degeneration of Riemann theta functions and of the Zhang-Kawazumi invariant with applications to a uniform Bogomolov conjecture
• Arithmetic bigness and a uniform Bogomolov-type result