The rational points on certain Abelian varieties over function fields

Sajad Salami

Published 2017-08-03Version 1

We prove a structure theorem on the Mordell-Weil group of Abelian varieties over function fields that arise as twists of Abelian varieties by cyclic covers of quasi-projective varieties, in terms of Prym varieties associated to the cyclic covers. Given integers $2\leq s \leq r$ and a polynomial $f(x)$ of degree $r$ with coefficients in a global field, we apply our result to the twists of Jacobian varieties of super-elliptic curves defined by affine equation $y^s=f(x)$ with cyclic covers of certain varieties to get super-elliptic Jacobians with large Mordell-Weil ranks.