New orders of torsion points in Jacobians of curves of genus 2 over the rational number field

DOI10.1134/S1064562412020330zbMath1319.11041OpenAlexW2092900004MaRDI QIDQ1761002

M. M. Petrunin, Vladimir Platonov

Publication date: 15 November 2012

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

Full work available at URL: https://doi.org/10.1134/s1064562412020330

Mathematics Subject Classification ID

Units and factorization (11R27) Arithmetic ground fields for curves (14H25) Jacobians, Prym varieties (14H40) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)]

Related Items (10)

Fundamental \(S\)-units in hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves ⋮ On the simplicity of Jacobians for hyperelliptic curves of genus 2 over the field of rational numbers with torsion points of high order ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On the torsion problem in Jacobians of curves of genus 2 over the rational number field ⋮ ОБОБЩЕННЫЕ ЯКОБИАНЫ И НЕПРЕРЫВНЫЕ ДРОБИ В ГИПЕРЭЛЛИПТИЧЕСКИХ ПОЛЯХ ⋮ On -units for valuations of the second degree in hyperelliptic fields ⋮ 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
• Curves of genus 2 with a rational torsion divisor of order 23
• Jacobians of some curves of genus 2: torsion and simplicity
• Large torsion subgroups of split Jacobians of curves of genus two or three
• Jacobians of Genus-2 Curves with a Rational Point of Order 11

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