Torsion on Jacobians of curves

This is a project within the EPSRC research area of Number Theory. The aim is develop new tools for computing torsion subgroups of Jacobians of curves. This will have applications to computing Galois representations, Mordell-Weil groups and rational points on curves. The plan is to use complex or p-adic methods such as numerical analysis or Hensel lifting to obtain very accurate approximation of the torsion points, and then to use lattice-based algorithms to compute the torsion points algebraically.