Point counting on curves using a gonality preserving lift
Number Theory
2017-06-15 v3 Algebraic Geometry
Abstract
We study the problem of lifting curves from finite fields to number fields in a genus and gonality preserving way. More precisely, we sketch how this can be done efficiently for curves of gonality at most four, with an in-depth treatment of curves of genus at most five over finite fields of odd characteristic, including an implementation in Magma. We then use such a lift as input to an algorithm due to the second author for computing zeta functions of curves over finite fields using -adic cohomology.
Cite
@article{arxiv.1605.02162,
title = {Point counting on curves using a gonality preserving lift},
author = {Wouter Castryck and Jan Tuitman},
journal= {arXiv preprint arXiv:1605.02162},
year = {2017}
}