Geometrie d'Arakelov et hauteurs canoniques sur des varietes   semi-abeliennes
  Canonical heights and Arakelov geometry on semi-abelian varieties.   In this paper, we propose a construction of the canonical heights on an extension of an abelian variety by the multiplicative group, in the framework of Arakelov geometry. These canonical heights are the sum of some height coming from the abelian variety and something we call a relative height. We finally give some complements about the points whose relative height is zero. 
Antoine Chambert-Loir