Fundamental \(S\)-units in hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves

DOI10.1134/S1064562415060034zbMath1348.14083OpenAlexW2302262832MaRDI QIDQ265945

M. M. Petrunin, Vladimir Platonov

Publication date: 13 April 2016

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

Full work available at URL: https://doi.org/10.1134/s1064562415060034

zbMATH Keywords

hyperelliptic curvesJacobi varietiestorsion \(Q\)-points

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Jacobians, Prym varieties (14H40) Local ground fields in algebraic geometry (14G20) [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 (6)

Unnamed Item ⋮ О НЕКОТОРЫХ СВОЙСТВАХ НЕПРЕРЫВНЫХ ПЕРИОДИЧЕСКИХ ДРОБЕЙ С НЕБОЛЬШОЙ ДЛИНОЙ ПЕРИОДА, СВЯЗАННЫХ С ГИПЕРЭЛЛИПТИЧЕСКИМИ ПОЛЯМИ И S-ЕДИНИЦАМИ ⋮ On the finiteness of hyperelliptic fields with special properties and periodic expansion of \(\sqrt{f}\) ⋮ Vladimir Petrovich Platonov ⋮ \(S\)-units in hyperelliptic fields and periodicity of continued fractions ⋮ Groups of \(S\)-units and the problem of periodicity of continued fractions in hyperelliptic fields

Cites Work

• 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
• On the torsion problem in Jacobians of curves of genus 2 over the rational number field
• Number-theoretic properties of hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves over the rational number field
• Groups ofS-units in hyperelliptic fields and continued fractions

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