4 citations · 5 across the 3 of their papers we have counts for
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The modular height of an abelian variety and its finiteness property
Atsushi Moriwaki
In this note, we propose the modular height of an abelian variety defined over a field of finite type over Q. Moreover, we prove its finiteness property.
A note on polarizations of finitely generated fields
Atsushi Moriwaki
In our previous paper, we established Northcott's theorem for height functions over finitely generated fields. Unfortunately, Northcott's theorem on finitely generated fields does…
The canonical arithmetic height of subvarieties of an abelian variety over a finitely generated field
Atsushi Moriwaki
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 subvariet…
A generalization of conjectures of Bogomolov and Lang over finitely generated fields
Atsushi Moriwaki
Let K be a finitely generated field over Q, and A an abelian variety over K. Let <, > : A(K^a) x A(K^a) --> R be an arithmetic height pairing on A, where K^a is the algebric closur…
Arithmetic height functions over finitely generated fields
Atsushi Moriwaki
In this paper, we propose a new height function for a variety defined over a finitely generated field over Q. For this height function, we will prove Northcott's theorem and Bogomo…