|
Title:
|
Trisection for supersingular genur 2 curves in characteristic 2
|
|
Author:
|
Miret, Josep M. (Josep Maria); Pujolàs Boix, Jordi; Thériault, Nicolas
|
|
Notes:
|
By reversing reduction in divisor class arithmetic we provide efficient trisection algorithms for Jacobians of supersingular genus 2 curves over finite fields of characteristic 2. With our technique we obtain new results for these Jacobians: we show how to find their 3-torsion subgroup, we prove there is none with 3-torsion subgroup of rank 3 and we prove their the maximal 3-power order subgroup is isomorphic to either Z/3^vZ or (Z/3^{v/2}Z)^2 or (Z/3^{v/4}Z)^4, where v is the 3-adic valuation v3(#Jac(C)(F2^m}). Ours are the first trisection formulae available in literature. |
|
Subject(s):
|
-Hyperelliptic curve
-Supersingular
-Genus 2 |
|
Rights:
|
(c) American Institute of Mathematical Sciences (AIMS), 2014
info:eu-repo/semantics/restrictedAccess |
|
Document type:
|
article
publishedVersion |
|
Published by:
|
American Institute of Mathematical Sciences (AIMS)
|
|
Share:
|
|
