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Let A be an abelian variety defined over a number field k. We provide in this paper different decomposition formulas for the N\'eron-Tate height of k-rational points on A. We deduce a decomposition of the Faltings height of the variety A itself. We also produce a local decomposition of the self-intersection of the relative dualizing sheaf (\omega_C.\omega_C) when A is the jacobian of a curve C. We formulate in 2.4 a question of Bogomolov type on the space of principally polarized abelian varieties of dimension g.

Décompositions en hauteurs locales