---
title: "Bibliography"
canonical: "https://docs.magma-maths.org/AlgebraicGeometry/AlgebraicCurves/bibliography.html"
source: "https://docs.magma-maths.org/AlgebraicGeometry/AlgebraicCurves/bibliography.md"
part: "Algebraic Geometry"
chapter: "Algebraic Curves"
breadcrumbs:
  - {"title": "Magma Handbook", "source": "../../index.md"}
  - {"title": "Algebraic Geometry", "source": "../index-algebraic-geometry.md"}
  - {"title": "Algebraic Curves", "source": "index-algebraic-curves.md"}
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---

# Bibliography

<a id="cite-castrycktuitman"></a>
- **[CT17]** Wouter Castryck and Jan Tuitman. Point counting on curves using a gonality preserving lift. *The Quarterly Journal of Mathematics*, 2017.
<a id="cite-diem06"></a>
- **[Die]** C. Diem. “An Index Calculus Algorithm for Plane Curves of Small Degree.” 543–557.
<a id="cite-elk2000"></a>
- **[Elk]** N. Elkies. “Rational Points Near Curves and Small Nonzero $|x^3 - y^2|$ via Lattice Reduction.” 33–63.
<a id="cite-fulton"></a>
- **[Ful69]** William Fulton. *Algebraic Curves*. Volume of Mathematics Lecture Note Series. W. A. Benjamin, New York-Amsterdam, 1969.
<a id="cite-mike-harr-gen56-11"></a>
- **[Har13]** M. C. Harrison. Explicit solution by radicals, gonal maps and plane models of algebraic curves of genus 5 or 6. *J. Symb. Comp.*, 51:3–21, 2013.
<a id="cite-harrisonkedlayaalgorithm"></a>
- **[Har12]** Michael C. Harrison. An extension of Kedlaya's algorithm for hyperelliptic curves. *J. Symbolic Comput.*, 47(1):89–101, 2012.
<a id="cite-hartshorne"></a>
- **[Har77]** Robin Hartshorne. *Algebraic Geometry, GTM 52*. Springer, ASpringer, 1977.
<a id="cite-har15"></a>
- **[Har15]** David Harvey. Computing zeta functions of arithmetic schemes. *Proceedings of the London Mathematical Society*, 111(6):1379–1401, 2015. URL: [https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/plms/pdv056](https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/plms/pdv056), [arXiv:https://londmathsoc.onlinelibrary.wiley.com/doi/pdf/10.1112/plms/pdv056](https://arxiv.org/abs/https://londmathsoc.onlinelibrary.wiley.com/doi/pdf/10.1112/plms/pdv056), [doi:https://doi.org/10.1112/plms/pdv056](https://doi.org/https://doi.org/10.1112/plms/pdv056).
<a id="cite-hilsmy10"></a>
- **[HS10]** J. Hilmar and C. Smyth. Euclid Meets Bézout: Intersecting Algebraic Plane Curves with the Euclidean Algorithm. *The American Mathematical Monthly*, 117:250–260, (March) 2010.
<a id="cite-kyn22"></a>
- **[Kyn22]** Madeleine Kyng. Computing zeta functions of algebraic curves using Harvey's trace formula. *Res. Number Theory*, 8(4):Paper No. 100, 17, 2022. URL: [https://doi.org/10.1007/s40993-022-00398-7](https://doi.org/10.1007/s40993-022-00398-7), [doi:10.1007/s40993-022-00398-7](https://doi.org/10.1007/s40993-022-00398-7).
<a id="cite-kyn25"></a>
- **[Kyn25]** Madeleine Kyng. *Computing zeta functions of algebraic curves using Harvey's trace formula*. Dissertation, The University of New South Wales, May 2025. available at https://web.maths.unsw.edu.au/ davidharvey/research/kyng-thesis.pdf.
<a id="cite-minzlaff-phd"></a>
- **[Min13]** Moritz Minzlaff. *Frobenius-stable lattices in rigid cohomology of curves*. Dissertation, Technische Universität Berlin, 2013. URL: [http://dx.doi.org/10.14279/depositonce-3566](http://dx.doi.org/10.14279/depositonce-3566).
<a id="cite-schicho-sevilla-11"></a>
- **[SS]** J. Schicho and D. Sevilla. Effective radical parametrization of trigonal curves. Preprint: online at arXiv as arXiv:1104.2470v1[math.AG].
<a id="cite-schreyer-tonoli"></a>
- **[ST02]** Frank-Olaf Schreyer and Fabio Tonoli. Needles in a Haystack: Special Varieties via Small Fields. In Eisenbud and others, editors, *Computations in Algebraic Geometry with Macaulay2*, volume 8 of Springer Algorithms and Computation in Mathematics Series, 251–277. Springer-Verlag, 2002.
<a id="cite-stoll-cluster-reduction"></a>
- **[Sto11]** “Reduction theory of point clusters in projective space.”
<a id="cite-tuitmani"></a>
- **[Tui16]** Jan Tuitman. Counting points on curves using a map to $\bf{P}^1$. *Math. Comp.*, 85(298):961–981, 2016.
<a id="cite-tuitmanii"></a>
- **[Tui17]** Jan Tuitman. Counting points on curves using a map to $\bf{P}^1$, II. *Finite Fields Appl.*, 45:301–322, 2017.
<a id="cite-lintgeer"></a>
- **[vLvdG88]** J. H. van Lint and G. van der Geer. *Introduction to Coding Theory and Algebraic Geometry*. Volume 12 of DMV Seminar. Birkhaeuser, Basel, 1988.