Point counting on curves using a gonality preserving lift
- Author
- Wouter Castryck (UGent) and Jan Tuitman
- 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: http://hdl.handle.net/1854/LU-8568116
- 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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