Computing the Mordell-Weil Groups of Hyperelliptic Jacobians(Survey,<Special Topics>Activity Group "Algorithmic Number Theory and Its Applications")

Abstract

The set of rational points on an Abelian variety defined over a number field forms a finitely generated Abelian group and is called the Mordell-Weil group. For elliptic curves, various algorithms on the computation of the Mordell-Weil groups are known. Recently, these algorithms were generalized to the Jacobian varieties of hyperelliptic curves. In this article, we give a survey on the computation of the Mordell-Weil groups of the Jacobian varieties of hyperelliptic curves.