Computing class groups and gonalities of algebraic curves over finite fields

Maarten Derickx; Kenji Terao

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arXiv · 2602.17417

Computing class groups and gonalities of algebraic curves over finite fields

Maarten Derickx·Kenji Terao

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Abstract

We give practical algorithms for computing the divisor class group and the gonality of a curve over a finite field, achieving several orders of magnitude speedup over existing methods for sufficiently large genus or residue field. The approach relies on introducing a precomputation step involving power series-expansions, which allows for an efficient amortized computation of large numbers of Riemann-Roch spaces.

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Maarten Derickx, Kenji Terao. 2026-02-19. Computing class groups and gonalities of algebraic curves over finite fields. https://arxiv.org/abs/2602.17417

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