The rational points on certain Abelian varieties over function fields

2017/08/03 by Salami, Sajad · 2 citations
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1708.01192

Abstract

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 associated to the cyclic covers, we prove a structure theorem on their Mordell-Weil group. Our results give an explicit method for construction of elliptic curves, hyper- and super-elliptic Jacobians that have large ranks over function fields of certain varieties.

Cited by

• Rank of Jacobian Varieties of Curves y^s=x(ax^r+b)
• On the Rank of Jacobian Varieties of the Curves y^s=ax^r+b

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