Twists of Albanese varieties over function fields with large ranks

TL;DR

This paper constructs abelian varieties with large Mordell-Weil ranks over function fields by generalizing Prym varieties and analyzing twists of Albanese varieties via covers of projective space.

Contribution

It introduces a higher-dimensional generalization of Prym varieties and applies a structure theorem to produce abelian varieties with large ranks over function fields.

Findings

Constructed abelian varieties with large Mordell-Weil ranks

Generalized Prym varieties to higher dimensions

Applied results to twists of Albanese varieties

Abstract

In this paper we construct abelian varieties of large Mordell-Weil rank over function fields. We achieve this by using a generalization of the notion of Prym variety to higher dimensions and a structure theorem for the Mordell-Weil group of abelian varieties over function fields proven in our previous works. We consider abelian and dihedral covers of the projective space and apply the above results to the twists of their Albanese varieties.