Local units, elliptic units, Heegner points and elliptic curves

DOI10.1007/BF01388915zbMath0623.14006OpenAlexW2049859779MaRDI QIDQ1091437

Karl Rubin

Publication date: 1987

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143460

zbMATH Keywords

elliptic curvecomplex multiplicationHeegner pointsBirch and Swinnerton-Dyer conjectureelliptic unitsIwasawa algebraTate- Shafarevich group

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Complex multiplication and abelian varieties (14K22) Cyclotomic extensions (11R18)

Related Items (12)

Construction of anti-cyclotomic Euler systems of modular abelian varieties, and the ranks of their Mordell-Weil groups ⋮ Ranks of the rational points of abelian varieties over ramified fields, and Iwasawa theory for primes with non-ordinary reduction ⋮ Supersingular elliptic curves over \(\mathbb{Z}_p\)-extensions ⋮ On the Iwasawa theory of CM fields for supersingular primes ⋮ Weak Leopoldt's conjecture for Hecke characters of imaginary quadratic fields ⋮ Anticyclotomic Iwasawa theory of abelian varieties of \(\mathrm{GL}_2\)-type at non-ordinary primes ⋮ The ``main conjectures of Iwasawa theory for imaginary quadratic fields ⋮ Iwasawa theory for modular forms at supersingular primes ⋮ Théorie d'Iwasawa p-adique locale et globale. (Local and global p-adic Iwasawa theory) ⋮ Rubin's conjecture on local units in the anticyclotomic tower at inert primes ⋮ CODIMENSION TWO CYCLES IN IWASAWA THEORY AND ELLIPTIC CURVES WITH SUPERSINGULAR REDUCTION ⋮ Unnamed Item

Cites Work

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• On the L-functions of canonical Hecke characters of imaginary quadratic fields. II
• On \(L\)-functions of elliptic curves and anticyclotomic towers
• Division values in local fields
• Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur
• On two variable p-adic L-functions
• On the conjecture of Birch and Swinnerton-Dyer
• On norm maps for one dimensional formal groups. III
• Higher explicit reciprocity laws
• On the structure of certain Galois groups
• Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer
• On Elliptic Curves with Complex Multiplication as Factors of the Jacobians of Modular Function Fields
• On the Birch and Swinnerton-Dyer conjecture

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