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 $(A,\lambda )$ .

Tropical moments of tropical Jacobians

“…For example, we have the following application concerning the computation of Arakelov heights attached to principally polarized abelian varieties defined over a number field. For more background and for terminology used in this section, we refer to [14].…”