The canonical arithmetic height of subvarieties of an abelian variety over a finitely generated field

Details The canonical arithmetic height of subvarieties of an abelian variety over a finitely generated field The canonical arithmetic height of subvarieties of an abelian variety over a finitely generated field

1999-10-19

arxiv.org/abs/math/9910090v1

Mathematics

Number Theory

20 pages, typeseted by AmSLaTeX

Scientific paper

This paper is the sequel of our paper "Arithmetic height functions over finitely generated fields" (cf. math.NT/9809016). In this paper, we define the canonical height of subvarieties of an abelian variety over a finitely generated field over Q. We also prove that the canonical height of a subvariety is zero if and only if it is a translation of an abelian subvariety by a torsion point.

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