On the main conjecture of Iwasawa theory for imaginary quadratic fields

DOI10.1007/BF01410205zbMath0673.12004OpenAlexW4234319238WikidataQ122860643 ScholiaQ122860643MaRDI QIDQ1120623

Karl Rubin

Publication date: 1988

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

Full work available at URL: https://eudml.org/doc/143614

zbMATH Keywords

fieldsIwasawa theoryTate-Shafarevich groupconjectureelliptic curve with complex multiplicationimaginary quadraticIwasawa main

Mathematics Subject Classification ID

Quadratic extensions (11R11) Elliptic curves (14H52) Complex multiplication and abelian varieties (14K22) Cyclotomic extensions (11R18)

Related Items

GLOBAL UNITS MODULO ELLIPTIC UNITS AND IDEAL CLASS GROUPS, Introduction to the Conjectures of Birch and Swinnerton-Dyer, Unnamed Item, Construction of anti-cyclotomic Euler systems of modular abelian varieties, and the ranks of their Mordell-Weil groups, On the structure of the module of Euler systems for a \(p\)-adic representation, On the higher Fitting ideals of Iwasawa modules of ideal class groups over real abelian fields, Image of \(\varLambda \)-adic Galois representations modulo \(p\), On the two-variables main conjecture for extensions of imaginary quadratic fields, Selmer varieties for curves with CM Jacobians, Weak Leopoldt's conjecture for Hecke characters of imaginary quadratic fields, Some remarks on the two-variable Main Conjecture of Iwasawa theory for elliptic curves without complex multiplication, The equivariant Tamagawa number conjecture for abelian extensions of imaginary quadratic fields, On the anticyclotomic main conjecture, The ``main conjectures of Iwasawa theory for imaginary quadratic fields, Geometry of the eigencurve at CM points and trivial zeros of Katz \(p\)-adic \(L\)-functions, The structure of Selmer groups, Bernoulli-Hurwitz numbers, Wieferich primes and Galois representations, \(p\)-adic \(L\)-functions and Selmer varieties associated to elliptic curves with complex multiplication, Tate–Shafarevich groups in anticyclotomic ℤ_p-extensions at supersingular primes, Systèmes d'Euler \(p\)-adiques et théorie d'Iwasawa. (\(p\)-adic Euler systems and Iwasawa theory.), The Conjecture of Birch and Swinnerton-Dyer, Unnamed Item, Big Galois representations and -adic -functions, On the passage from local to global in number theory, Class groups of abelian fields, and the main conjecture, General Selmer groups and critical values of Hecke \(L\)-functions

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