On the simplicity of Jacobians for hyperelliptic curves of genus 2 over the field of rational numbers with torsion points of high order

DOI10.1134/S1064562413030216zbMath1278.14045OpenAlexW2052980309MaRDI QIDQ378199

M. M. Petrunin, V. S. Zhgun, Vladimir Platonov

Publication date: 11 November 2013

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562413030216

zbMATH Keywords

hyperelliptic curvesJacobianstorsion pointsgenus two curves

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves (14H52)

Related Items (5)

Unnamed Item ⋮ ОБОБЩЕННЫЕ ЯКОБИАНЫ И НЕПРЕРЫВНЫЕ ДРОБИ В ГИПЕРЭЛЛИПТИЧЕСКИХ ПОЛЯХ ⋮ An infinite family of curves of genus 2 over the field of rational numbers whose Jacobian varieties contain rational points of order 28 ⋮ New curves of genus 2 over the field of rational numbers whose Jacobians contain torsion points of high order ⋮ Genus-2 Jacobians with torsion points of large order

Cites Work

• A new local-global principle for quadratic function fields
• Arithmetic of quadratic fields and torsion in Jacobians
• New orders of torsion points in Jacobians of curves of genus 2 over the rational number field
• Jacobians of some curves of genus 2: torsion and simplicity
• On the torsion problem in Jacobians of curves of genus 2 over the rational number field

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