Title: The rational points on certain Abelian varieties over function fields,
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.