Inventiones mathematicae

, Volume 93, Issue 3, pp 701–713 | Cite as

On the main conjecture of Iwasawa theory for imaginary quadratic fields

  • Karl Rubin
Article

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References

  1. 1.
    Coates, J.: Infinite descent on elliptic curves. In: Arithmetic and Geometry, papers dedicated to I.R. Shafarevich on the occasion of his 60th birthday. Prog. Math.35, 107–136. Boston: Birkhäuser (1983)Google Scholar
  2. 2.
    Coates, J., Goldstein, C.: Some remarks on the main conjecture for elliptic curves with complex multiplication. Am J. Math.105, 337–366 (1983)Google Scholar
  3. 3.
    Coates, J., Wiles, A.: On the conjecture of Birch and Swinnerton-Dyer. Invent. Math.39, 223–251 (1977)Google Scholar
  4. 4.
    Coates, J., Wiles, A.: Onp-adicL-functions and elliptic units. J. Austr. Math. Soc.26, 1–25 (1978)Google Scholar
  5. 5.
    de Shalit, E.: The Iwasawa Theory of Elliptic Curves with Complex Multiplication. Perspec. Math.3, Orlando: Academic Press (1987)Google Scholar
  6. 6.
    Gillard, R.: FonctionsL p-adiques des corps quadratiques imaginaires et de leurs extensions abéliennes. J. Reine Angew. Math.358, 76–91 (1986)Google Scholar
  7. 7.
    Goldstein, C., Schappacher, N.: Séries d'Eisenstein et fonctionsL de courbes elliptiques à multiplication complexe. J. Reine Angew. Math.327, 184–218 (1981)Google Scholar
  8. 8.
    Greenberg, R.: On the structure of certain Galois groups. Invent Math.47, 85–99 (1978)Google Scholar
  9. 9.
    Greenberg, R.: On the Birch and Swinnerton-Dyer conjecture. Invent. Math.72, 241–265 (1983)Google Scholar
  10. 10.
    Greenberg, R.: Elliptic curves andZ p-extensions (To appear)Google Scholar
  11. 11.
    Iwasawa, K.: OnZ l-extensions of algebraic number fields. Ann. Math.98, 246–326 (1973)Google Scholar
  12. 12.
    Mazur, B.: Rational points of abelian varieties with values in towers of number fields. Invent. Math.18, 183–266 (1972)Google Scholar
  13. 13.
    Perrin-Riou, B.: Arithmétique des courbes elliptiques et théorie d'Iwasawa. Mém. Soc. Math. Fr.17 (1984)Google Scholar
  14. 14.
    Perrin-Riou, B.: Points de Heegner et dérivées de fonctionsLp-adiques. Invent. Math.89, 455–510 (1987)Google Scholar
  15. 15.
    Rohrlich, D.: OnL-functions of elliptic curves and cyclotomic towers. Invent. Math.75, 409–423 (1984)Google Scholar
  16. 16.
    Rohrlich, D.:L-functions and division towers. Math. Ann. (To appear)Google Scholar
  17. 17.
    Rubin, K.: Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer. Invent. Math.64, 455–470 (1981)Google Scholar
  18. 18.
    Rubin, K.: Global units and ideal class groups. Invent. Math.89, 511–526 (1987)Google Scholar
  19. 19.
    Rubin, K.: Tate-Shafarevich groups andL-functions of elliptic curves with complex multiplication. Invent. Math.89, 527–560 (1987)Google Scholar
  20. 20.
    Serre, J-P., Tate, J.: Good reduction of abelian varieties. Ann. Math.88, 492–517 (1968)Google Scholar
  21. 21.
    Shimura, G.: On elliptic curves with complex multiplication as factors of the jacobians of modular function fields. Nagoya Math. J.43, 199–208 (1971)Google Scholar
  22. 22.
    Thaine, F.: On the ideal class groups of real abelian number fields (To appear)Google Scholar
  23. 23.
    Wintenberger, J-P.: Structure galoisienne de limites projectives d'unités locales. Comp. Math.42, 89–103 (1981)Google Scholar
  24. 24.
    Yager, R.: On two variablep-adicL-functions. Ann. Math.115, 411–449 (1982)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Karl Rubin
    • 1
  1. 1.Department of MathematicsOhio State UniversityColumbusUSA

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