The canonical arithmetic height of subvarieties of an abelian variety over a finetely generated field
Copyright policy )The canonical arithmetic height of subvarieties of an abelian variety over a finetely generated field
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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Mathematics - Number Theory, abelian variety, Heights, torsion point, 14G25, canonical height, 14G40, Abelian varieties of dimension \(> 1\), Mathematics - Algebraic Geometry, 11G35;14G25;14G40, Arithmetic ground fields for abelian varieties, subvarieties, FOS: Mathematics, 11G35, Number Theory (math.NT), Arithmetic varieties and schemes; Arakelov theory; heights, Varieties over global fields, Algebraic Geometry (math.AG)
Mathematics - Number Theory, abelian variety, Heights, torsion point, 14G25, canonical height, 14G40, Abelian varieties of dimension \(> 1\), Mathematics - Algebraic Geometry, 11G35;14G25;14G40, Arithmetic ground fields for abelian varieties, subvarieties, FOS: Mathematics, 11G35, Number Theory (math.NT), Arithmetic varieties and schemes; Arakelov theory; heights, Varieties over global fields, Algebraic Geometry (math.AG)
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