Arithmetic on Curves of Genus 1 : III. The Tate-Šafarevič and Selmer Groups

DOI10.1112/plms/s3-12.1.259zbMath0106.03705OpenAlexW2053658212WikidataQ56003249 ScholiaQ56003249MaRDI QIDQ3291625

J. W. S. Cassels

Publication date: 1962

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/plms/s3-12.1.259

zbMATH Keywords

Tate-Shafarevich groupSelmer groupWeil-Chatelet grouparithmetic on curves of genus one

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Curves over finite and local fields (11G20)

Related Items (15)

Derived heights and generalized Mazur-Tate regulators ⋮ Weil–Châtelet divisible elements in Tate–Shafarevich groups I: The Bashmakov problem for elliptic curves over ⋮ Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero ⋮ Integral points on the congruent number curve ⋮ The local-global principle for divisibility in CM elliptic curves ⋮ Local-global principles for Weil–Châtelet divisibility in positive characteristic ⋮ On 7-division fields of CM elliptic curves ⋮ Root numbers and parity phenomena ⋮ The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields ⋮ Computational verification of the Birch and Swinnerton-Dyer conjecture for individual elliptic curves ⋮ Arithmetic on algebraic varieties ⋮ Théorie d'Iwasawa p-adique locale et globale. (Local and global p-adic Iwasawa theory) ⋮ The Selmer groups of elliptic curves. ⋮ Divisibility questions in commutative algebraic groups ⋮ Local-global questions for divisibility in commutative algebraic groups

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