Curves in characteristic 2 with non-trivial 2-torsion
- Author
- Wouter Castryck (UGent) , Marco Streng and Damiano Testa
- Organization
- Abstract
- Cais, Ellenberg and Zureick-Brown recently observed that over finite fields of characteristic two, all sufficiently general smooth plane projective curves of a given odd degree admit a non-trivial rational 2-torsion point on their Jacobian. We extend their observation to curves given by Laurent polynomials with a fixed Newton polygon, provided that the polygon satisfies a certain combinatorial property. We also show that in each of these cases, if the curve is ordinary, then there is no need for the words "sufficiently general". Our treatment includes many classical families, such as hyperelliptic curves of odd genus and C-a,C-b curves. In the hyperelliptic case, we provide alternative proofs using an explicit description of the 2-torsion subgroup.
- Keywords
- EXTRA AUTOMORPHISMS, FINITE-FIELDS, HYPERELLIPTIC CURVES, ARTIN-SCHREIER CURVES, even characteristic, toric surfaces, Algebraic curves, POINTS, NUMBER, RANK
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-5825467
- MLA
- Castryck, Wouter, et al. “Curves in Characteristic 2 with Non-Trivial 2-Torsion.” ADVANCES IN MATHEMATICS OF COMMUNICATIONS, vol. 8, no. 4, 2014, pp. 479–95, doi:10.3934/amc.2014.8.479.
- APA
- Castryck, W., Streng, M., & Testa, D. (2014). Curves in characteristic 2 with non-trivial 2-torsion. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 8(4), 479–495. https://doi.org/10.3934/amc.2014.8.479
- Chicago author-date
- Castryck, Wouter, Marco Streng, and Damiano Testa. 2014. “Curves in Characteristic 2 with Non-Trivial 2-Torsion.” ADVANCES IN MATHEMATICS OF COMMUNICATIONS 8 (4): 479–95. https://doi.org/10.3934/amc.2014.8.479.
- Chicago author-date (all authors)
- Castryck, Wouter, Marco Streng, and Damiano Testa. 2014. “Curves in Characteristic 2 with Non-Trivial 2-Torsion.” ADVANCES IN MATHEMATICS OF COMMUNICATIONS 8 (4): 479–495. doi:10.3934/amc.2014.8.479.
- Vancouver
- 1.Castryck W, Streng M, Testa D. Curves in characteristic 2 with non-trivial 2-torsion. ADVANCES IN MATHEMATICS OF COMMUNICATIONS. 2014;8(4):479–95.
- IEEE
- [1]W. Castryck, M. Streng, and D. Testa, “Curves in characteristic 2 with non-trivial 2-torsion,” ADVANCES IN MATHEMATICS OF COMMUNICATIONS, vol. 8, no. 4, pp. 479–495, 2014.
@article{5825467,
abstract = {{Cais, Ellenberg and Zureick-Brown recently observed that over finite fields of characteristic two, all sufficiently general smooth plane projective curves of a given odd degree admit a non-trivial rational 2-torsion point on their Jacobian. We extend their observation to curves given by Laurent polynomials with a fixed Newton polygon, provided that the polygon satisfies a certain combinatorial property. We also show that in each of these cases, if the curve is ordinary, then there is no need for the words "sufficiently general". Our treatment includes many classical families, such as hyperelliptic curves of odd genus and C-a,C-b curves. In the hyperelliptic case, we provide alternative proofs using an explicit description of the 2-torsion subgroup.}},
author = {{Castryck, Wouter and Streng, Marco and Testa, Damiano}},
issn = {{1930-5346}},
journal = {{ADVANCES IN MATHEMATICS OF COMMUNICATIONS}},
keywords = {{EXTRA AUTOMORPHISMS,FINITE-FIELDS,HYPERELLIPTIC CURVES,ARTIN-SCHREIER CURVES,even characteristic,toric surfaces,Algebraic curves,POINTS,NUMBER,RANK}},
language = {{eng}},
number = {{4}},
pages = {{479--495}},
title = {{Curves in characteristic 2 with non-trivial 2-torsion}},
url = {{http://doi.org/10.3934/amc.2014.8.479}},
volume = {{8}},
year = {{2014}},
}
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