  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.
