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arXiv · 1604.04563

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

David Holmes
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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 generalisation 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.

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David Holmes. 2016-04-15. Torsion points and height jumping in higher-dimensional families of abelian varieties. https://arxiv.org/abs/1604.04563

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