Week 17.02.2025 – 23.02.2025

Title: Computing torsion points on Jacobians of Curves
Abstract: Points on the Jacobian of a curve can easily be constructed when points on the curve are known. We may ask whether one could compute points on the Jacobian without prior knowledge of any points on the curve. In this talk we discuss a method for computing the group of 3-torsion points on the Jacobian of a genus 3 curve. We use elementary geometry to derive a system of equations whose equations parametrise 3-torsion points and use complex analysis and lattice reduction to find precise expressions for the solutions. Time permitting, I will discuss an application of this to computing the local conductor exponent at 2.