Geometrie d'Arakelov et hauteurs canoniques sur des varietes semi-abeliennes

Details Geometrie d'Arakelov et hauteurs canoniques sur des varietes semi-abeliennes Geometrie d'Arakelov et hauteurs canoniques sur des varietes semi-abeliennes

1998-05-25

arxiv.org/abs/math/9805111v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

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.

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