Linda Frey

Elliptic curves, small heights and an outlook to genus two

Finding elements of small height in a field or proving there is no possibility to find them is an active field of research. There are fields where there is a lower bound for the height (Bogomolov fields) and today we will talk about one of them: Q(E_tor), which is the field we get by adjoining all coordinates of torsion points of an elliptic curve. We will state some results, a generalization and give a short outlook on what could be done with heights and genus 2 curves.