Dr. Sajad Salami from Universidade Estadual do Rio de Janeiro, Brasil will give the following talk at IPM, on September 22, 2018 (31 Shahrivar 1397):
Title: The rational points of certain Abelian varieties over function fields
Abstract: 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.