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Title: Curves in characteristic 2 with non-trivial 2-torsion
Authors: Castryck, Wouter * ×
Streng, Marco *
Testa, Damiano * #
Issue Date: 2014
Publisher: American Institute of Mathematical Sciences
Series Title: Advances in Mathematics of Communications
Conference: GeoCrypt location:Papeete, Tahiti date:7-11 October 2013
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 C_ab curves. In the hyperelliptic case, we provide alternative proofs using an explicit description of the 2-torsion subgroup.
ISSN: 1930-5346
Publication status: accepted
KU Leuven publication type: IT
Appears in Collections:Algebra Section
* (joint) first author
× corresponding author
# (joint) last author

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