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

Atsushi Moriwaki

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arXiv · math/9910090

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

Atsushi Moriwaki

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Abstract

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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Atsushi Moriwaki. 1999-10-19. The canonical arithmetic height of subvarieties of an abelian variety over a finitely generated field. https://arxiv.org/abs/math/9910090

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