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Point counting on curves using a gonality preserving lift

Author
Organization
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 p-adic cohomology.
Keywords
HYPERELLIPTIC CURVES, KEDLAYAS ALGORITHM, CANONICAL CURVES, CHARACTERISTIC-P, LINEAR PENCILS, EXTENSION, PARAMETRIZATION, FAMILIES, SYSTEM

Citation

Please use this url to cite or link to this publication:

MLA
Castryck, Wouter, and Jan Tuitman. “Point Counting on Curves Using a Gonality Preserving Lift.” QUARTERLY JOURNAL OF MATHEMATICS, vol. 69, no. 1, 2018, pp. 33–74, doi:10.1093/qmath/hax031.
APA
Castryck, W., & Tuitman, J. (2018). Point counting on curves using a gonality preserving lift. QUARTERLY JOURNAL OF MATHEMATICS, 69(1), 33–74. https://doi.org/10.1093/qmath/hax031
Chicago author-date
Castryck, Wouter, and Jan Tuitman. 2018. “Point Counting on Curves Using a Gonality Preserving Lift.” QUARTERLY JOURNAL OF MATHEMATICS 69 (1): 33–74. https://doi.org/10.1093/qmath/hax031.
Chicago author-date (all authors)
Castryck, Wouter, and Jan Tuitman. 2018. “Point Counting on Curves Using a Gonality Preserving Lift.” QUARTERLY JOURNAL OF MATHEMATICS 69 (1): 33–74. doi:10.1093/qmath/hax031.
Vancouver
1.
Castryck W, Tuitman J. Point counting on curves using a gonality preserving lift. QUARTERLY JOURNAL OF MATHEMATICS. 2018;69(1):33–74.
IEEE
[1]
W. Castryck and J. Tuitman, “Point counting on curves using a gonality preserving lift,” QUARTERLY JOURNAL OF MATHEMATICS, vol. 69, no. 1, pp. 33–74, 2018.
@article{8568116,
  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 p-adic cohomology.}},
  author       = {{Castryck, Wouter and Tuitman, Jan}},
  issn         = {{0033-5606}},
  journal      = {{QUARTERLY JOURNAL OF MATHEMATICS}},
  keywords     = {{HYPERELLIPTIC CURVES,KEDLAYAS ALGORITHM,CANONICAL CURVES,CHARACTERISTIC-P,LINEAR PENCILS,EXTENSION,PARAMETRIZATION,FAMILIES,SYSTEM}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{33--74}},
  title        = {{Point counting on curves using a gonality preserving lift}},
  url          = {{http://dx.doi.org/10.1093/qmath/hax031}},
  volume       = {{69}},
  year         = {{2018}},
}

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