Hyperelliptic curves in characteristic 2
| dc.creator | Scholten, Jasper | |
| dc.creator | Zhu, Hui June | |
| dc.date | 2000-12-19 | |
| dc.date | 2001-05-03 | |
| dc.date.accessioned | 2026-07-25T23:03:36Z | |
| dc.description | In this paper we prove that there are no hyperelliptic supersingular curves over F_2bar of genus 2^n-1 for any integer n>1. Let g be a natural number, and h=floor(log_2(g+1)+1). Let X be a hyperelliptic curve over F_2bar of genus g>2 and 2-rank zero, given by an affine equation y^2-y=c_{2g+1} x^{2g+1} +...+ c_1 x. We prove that the first slope of the Newton polygon of X is bigger than or equal to 1/h. We also prove that the equality holds if (I) g<2^h-2, c_{2^h-1} is nonzero; or (II) g=2^h-2, c_{2^h-1} or c_{3(2^{h-1})-1} is nonzero. We prove that genus-4 hyperelliptic curve over F_2bar are precisely those with equations y^2 - y = x^9 + a x^5 + b x^3. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0012178 | |
| dc.identifier | http://arxiv.org/abs/math/0012178 | |
| dc.identifier | Inter. Math. Research Notices, 17 (2002), 905-917. | |
| dc.identifier.uri | https://dspace.dare.co.zw/handle/123456789/95113 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.title | Hyperelliptic curves in characteristic 2 | |
| dc.type | text |