Refined quadratic Chabauty criteria for hyperelliptic curves
Lee Berry (King's College London)
Wednesday 20th November 16:00-17:00 Maths 311B
Abstract
The Chabauty-Coleman method is a powerful tool for explicitly computing rational points on higher genus curves, though it is limited to cases where the Mordell-Weil rank of the Jacobian is less than the genus. To broaden its applicability, Kim introduced a significant generalisation of this method, which has led to effective instances such as the method of quadratic Chabauty for rational points. In this talk, we will give a brief overview of Chabauty-Kim theory and discuss forthcoming work in improving the applicability of the quadratic Chabauty method, particularly to hyperelliptic curves.
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