Abstract:

By a famous result of André Weil the Mordell-Weil group of k-rational points on an abelian variety over a number field k is finitely generated. In general there is no efficient way known to compute this group. If we restrict to the case of the Jacobian variety associated to a hyperelliptic curve, then there is a collection of methods that in many examples can be used to make these computations explicit. In this talk we look at some of these methods and what is necessary to implement them using hyperelliptic curves of genus 4 as an example. A special focus will be given towards the Kummer variety of such a curve.