p-torsion in elliptic curves over subfields of \({\mathbb Q}(\mu _ p)\)

DOI10.1007/BF01456341zbMath0626.14024MaRDI QIDQ580460

Sheldon Kamienny

Publication date: 1988

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

Full work available at URL: https://eudml.org/doc/164379

zbMATH Keywords

cyclotomic fieldG-curvenon-existence of non-cuspidal rational pointsp-torsion in elliptic curves

Mathematics Subject Classification ID

Rational points (14G05) Arithmetic ground fields for curves (14H25) Special algebraic curves and curves of low genus (14H45) Elliptic curves (14H52) Cyclotomic extensions (11R18)

Related Items (2)

Torsion points on elliptic curves over fields of low degree ⋮ Sur la nature non-cyclotomique des points d'ordre fini des courbes elliptiques. (On the noncyclotomic nature of finite-order points of elliptic curves). With an appendix by E. Kowalski and P. Michel

Cites Work

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• On the torsion subgroups of elliptic curves over toally real fields
• Torsion points on elliptic curves over all quadratic fields
• Points of order \(p\) on elliptic curves over \(\mathbb Q(\sqrt p)\)
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• Modular curves and the Eisenstein ideal
• Good reduction of abelian varieties
• Rational points on modular curves and abelian varieties.
• Torsion points on elliptic curves over all quadratic fields. II
• Schémas en groupes de type $(p,\ldots,p)$
• Les Schémas de Modules de Courbes Elliptiques

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