IPM Calendar 
Thursday 18 July 2019   Today  
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. ...