The rational points on certain Abelian varieties over function fields

JOURNAL OF NUMBER THEORY

卷:195

Article

Salami, Sajad¹ 

[1] Univ Estado Rio De Janeiro, Inst Matemat & Estat, Rio De Janeiro, RJ, Brazil

关键词: Mordell-Weil rank;    Abelian variety;    Function field of varieties;    Prym varieties of the cyclic covers;    Jacobian variety;   

DOI  :  10.1016/j.jnt.2018.06.008

来源: Elsevier

【 摘 要 】

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 of the cyclic covers, we prove 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free