Curves of genus two over fields of even characteristic

DOI10.1007/s00209-004-0750-0zbMath1097.11033arXivmath/0210105OpenAlexW2076161163MaRDI QIDQ1775191

Jordi Pujolàs, Gabriel Cardona, Enric Nart Viñals

Publication date: 4 May 2005

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0210105

zbMATH Keywords

finite fieldcurvegenus twoIgusa invariant

Mathematics Subject Classification ID

Curves over finite and local fields (11G20) Other nonalgebraically closed ground fields in algebraic geometry (14G27) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (12)

Non-hyperelliptic curves of genus three over finite fields of characteristic two ⋮ Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects ⋮ A review on the isomorphism classes of hyperelliptic curves of genus 2 over finite fields admitting a Weierstrass point ⋮ Isomorphism classes of hyperelliptic curves of genus 2 over finite fields with characteristic 2 ⋮ Halving for the 2-Sylow subgroup of genus 2 curves over binary fields ⋮ Cyclic Isogenies for Abelian Varieties with Real Multiplication ⋮ Trisection for non-supersingular genus 2 curves in characteristic 2 ⋮ Representations of \(G_k\)-groups and twists of the genus two curve \(y^2=x^5 - x\) ⋮ Families of genus 2 curves with small embedding degree ⋮ Abelian Surfaces over Finite Fields as Jacobians ⋮ Hyperelliptic curves of genus three over finite fields of even characteristic ⋮ Computing the 2-adic canonical lift of genus 2 curves

Cites Work

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• Algebraic function fields and codes
• Hyperelliptic cryptosystems
• On the number of curves of genus 2 over a finite field.
• Arithmetic variety of moduli for genus two
• Supersingular Curves of Genus 2 over Finite Fields of Characteristic 2

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