Hensel-lifting torsion points on jacobians and galois representations

Abstract

Let ρ be a mod l Galois representation. We show how to compute ρ explicitly, given the characteristic polynomial of the image of the Frobenius at one prime p and a curve C whose Jacobian contains ρ in its l-torsion. The main ingredient is a method to p-adically lift torsion points on a Jacobian in the framework of Makdisi's algorithms. © 2019 American Mathematical Society.