The rational points on certain Abelian varieties over function fields
Number Theory
2018-01-26 v4
Abstract
In this paper, we consider Abelian varieties over function fields that arise as twists of Abelian varieties by cyclic covers of irreducible quasi-projective varieties. Then, in terms of Prym varieties associated to the cyclic covers, we prove a structure theorem on their Mordell-Weil group. Our results give an explicit method for construction of elliptic curves, hyper- and super-elliptic Jacobians that have large ranks over function fields of certain varieties.
Cite
@article{arxiv.1708.01192,
title = {The rational points on certain Abelian varieties over function fields},
author = {Sajad Salami},
journal= {arXiv preprint arXiv:1708.01192},
year = {2018}
}