Torsion points and height jumping in higher-dimensional families of abelian varieties

Author(s):
Holmes, D.
Published
2019
Publication type
Article / Letter to editor

Abstract

In 1983, Silverman and Tate showed that the set of points in a 1-dimensional family of abelian varieties where a section of infinite order has “small height” is finite. We conjecture a generalization to higher-dimensional families, where we replace “finite” by “not Zariski dense.” We show that this conjecture would imply the uniform boundedness conjecture for torsion points on abelian varieties. We then prove a few special cases of this new conjecture.

Date issued
2019-06-20
Language
English
Is part of
International Journal of Number Theory (2019), Vol. 15, no. 09, p. 1801-1826
hdl
1887/77169
doi
10.1142/S179304211950101X