# Twists of the Albanese varieties of cyclic multiple planes with large ranks over higher dimension function fields

## TL;DR

This paper develops explicit methods to construct abelian varieties with large ranks over higher-dimensional function fields by applying a structure theorem relating Mordell-Weil groups, Prym varieties, and twists of Albanese varieties of cyclic multiple planes.

## Contribution

It introduces a concrete construction approach for abelian varieties with large ranks over higher-dimensional function fields, extending previous theoretical results.

## Key findings

- Explicit construction of high-rank abelian varieties over higher-dimensional function fields
- Application of Prym varieties to understand Mordell-Weil groups
- Demonstration of large rank examples via twists of Albanese varieties

## Abstract

In [17], we proved a structure theorem on the Mordell-Weil group of abelian varieties over function fields that arise as the twists of abelian varieties by the cyclic covers of projective varieties in terms of the Prym varieties associated with covers. In this paper, we provide an explicit way to construct the abelian varieties with large ranks over the higher dimension function fields. To do so, we apply the above-mentioned theorem to the twists of Albanese varieties of the cyclic multiple planes.