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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 69.1 (2018): 33–74. Print.
APA
Castryck, W., & Tuitman, J. (2018). Point counting on curves using a gonality preserving lift. QUARTERLY JOURNAL OF MATHEMATICS, 69(1), 33–74.
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.
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.
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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