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arXiv · 1708.01192

The rational points on certain Abelian varieties over function fields

Sajad Salami
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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.

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Sajad Salami. 2017-08-03. The rational points on certain Abelian varieties over function fields. https://arxiv.org/abs/1708.01192

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