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Curves in characteristic 2 with non-trivial 2-torsion
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Castryck, Wouter, Streng, Marco and Testa, Damiano (2014) Curves in characteristic 2 with non-trivial 2-torsion. Advances in Mathematics of Communications, 8 (4). pp. 479-495. doi:10.3934/amc.2014.8.479
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Official URL: https://doi.org/10.3934/amc.2014.8.479
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, the sufficiently general condition is implied by being ordinary. Our treatment includes many classical families, such as hyperelliptic curves of odd genus and Ca,b curves. In the hyperelliptic case, we provide alternative proofs using an explicit description of the 2-torsion subgroup.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Curves, Plane, Torsion theory (Algebra) | ||||||
| Journal or Publication Title: | Advances in Mathematics of Communications | ||||||
| Publisher: | American Institute of Mathematical Sciences (A I M S Press) | ||||||
| Official Date: | 2014 | ||||||
| Dates: |
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| Volume: | 8 | ||||||
| Number: | 4 | ||||||
| Page Range: | pp. 479-495 | ||||||
| DOI: | 10.3934/amc.2014.8.479 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 13 July 2018 | ||||||
| Date of first compliant Open Access: | 13 July 2018 | ||||||
| RIOXX Funder/Project Grant: |
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