Linearizing torsion classes in the Picard group of algebraic curves over finite fields

TL;DR

This paper presents methods for computing torsion points on Jacobians of algebraic curves over finite fields to facilitate the calculation of modular representations.

Contribution

It introduces algorithms for linearizing torsion classes in the Picard group of algebraic curves over finite fields.

Findings

Efficient computation of $ ext{ell}^k$-torsion points

Application to modular representation calculations

Improved algorithms for Jacobian torsion groups

Abstract

We address the problem of computing in the group of $\ell^k$-torsion rational points of the jacobian variety of algebraic curves over finite fields, with a view toward computing modular representations.