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Trisection for supersingular genur 2 curves in characteristic 2

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Issue date
2014
Author
Miret, Josep M. (Josep Maria)
Pujolàs Boix, Jordi
Thériault, Nicolas
Suggested citation
Miret, Josep M. (Josep Maria); Pujolàs Boix, Jordi; Thériault, Nicolas; . (2014) . Trisection for supersingular genur 2 curves in characteristic 2. Advances in Mathematics of Communications, 2014, vol. 8, núm. 4, 375-387. https://doi.org/10.3934/amc.2014.8.375.
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Abstract
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.
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http://hdl.handle.net/10459.1/48930
DOI
https://doi.org/10.3934/amc.2014.8.375
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Advances in Mathematics of Communications, 2014, vol. 8, núm. 4, 375-387
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