Faltings height and Néron-Tate height of a theta divisor

The two heights from the title are fundamental invariants associated to any principally polarized abelian variety defined over the field of algebraic numbers. We prove a formula that writes the difference of both in Arakelov style as a sum of some non-archimedean and archimedean contributions. The non-archimedean contributions are based on the notion of "second moment" of a polarized abelian variety defined over a complete discretely valued field. We define this notion using non-archimedean uniformization and Berkovich analytic theory of abelian varieties. Our formula completes earlier results due to Bost, Hindry, Autissier and Wagener. This is joint work with Farbod Shokrieh.