|Thursday 18 July 2019|
|Events for day: Saturday 22 September 2018|
| 14:00 - 15:00 Seminar|
The rational points of certain Abelian varieties over function fields
In this talk, we consider the set of rational points on Abelian varieties over function fields that arise as twists of Abelian varieties by cyclic covers of irreducible quasi-projective varieties. In terms of Prym varieties associated with the cyclic covers, we demonstrate a structure theorem on their Mordell-Weil group. Our results give an explicit method to construct elliptic curves, hyper- and super-elliptic Jacobians that have large ranks over function fields of certain varieties. ...