Arithmetic of quadratic fields and torsion in Jacobians

DOI10.1134/S1064562410010163zbMath1217.11094MaRDI QIDQ606500

Vladimir Platonov

Publication date: 17 November 2010

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

zbMATH Keywords

unitslocal-global principle

Mathematics Subject Classification ID

Quadratic extensions (11R11) Units and factorization (11R27) Polynomials (irreducibility, etc.) (11R09)

Related Items (10)

Fundamental \(S\)-units in hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves ⋮ \(S\)-units and periodicity of continued fractions in hyperelliptic fields ⋮ 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 the Periodicity of Continued Fractions in Hyperelliptic Fields ⋮ New curves of genus 2 over the field of rational numbers whose Jacobians contain torsion points of high order ⋮ New orders of torsion points in Jacobians of curves of genus 2 over the rational number field

Cites Work

• Continued fractions and \(S\)-units in function fields
• Groups of \(S\)-units in hyperelliptic fields
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• Bounds for the torsion of elliptic curves over number fields
• Multiples of Points on Elliptic Curves and Continued Fractions

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