References
Coates, J.: Infinite descent on elliptic curves with complex multiplication. In: Arithmetic and Geometry, papers dedicated to I.R. Shafarevich on the occasion of his 60th birthday. Prog. Math. vol. 35, pp. 107–136 (1983)
Coates, J., Wiles, A.: On the conjecture of Birch and Swinnerton-Dyer. Invent. Math.39, 223–251 (1977)
Coates, J., Wiles, A.: Onp-adicL-functions and elliptic units. J. Aust. Math. Soc., Ser.A26, 1–25 (1978)
de Shalit, E.: The Iwasawa theory of elliptic curves with complex multiplication. Perspect. Math. vol. 3 (1987)
Gillard, R.: Remarques sur les unités cyclotomiques et les unités elliptiques. J. Number Theory11, 21–48 (1979)
Gillard, R.: FonctionsL p-adiques des corps quadratiques imaginaires et de leurs extensions abéliennes. J. Reine Angew. Math.358, 76–91 (1986)
Greenberg, R.: On the structure of certain Galois groups. Invent. Math.47, 85–99 (1978)
Greenberg, R.: On the Birch and Swinnerton-Dyer conjecture. Invent. Math.72, 241–265 (1983)
Gross, B.: On the conjecture of Birch and Swinnerton-Dyer for elliptic curves with complex multiplication. In: Number Theory related to Fermat's Last Theorem, Prog. Math. vol. 26, pp. 219–236 (1982)
Gross, B., Zagier, D.: Heegner points and derivatives ofL-series. Invent. Math.84, 225–320 (1986)
Iwasawa, K.: OnZ 1-extensions of algebraic number fields. Ann. Math.98, 246–326 (1973)
Katz, N.:p-adic interpolation of real analytic Eisentein series. Ann. Math.104, 459–571 (1976)
Kolyvagin, V.A.: Finiteness ofE(Q) and III (E,Q) for a class of Weil curves. Izv. Akad. Nauk SSSR, Ser Mat.52, 522–540 (1988), (Russian); Math. USSR, Izv.32, 523–542 (1989) (English)
Kolyvagin, V.A.: Euler systems. (To appear)
Mazur, B.: Rational points of abelian varieties with values in towers of number fields. Invent. Math.18, 183–266 (1972)
Mazur, B., Swinnerton-Dyer, P.: Arithmetic of Weil curves. Invent. Math.25, 1–61 (1974)
Mazur, B., Wiles, A.: Class fields of abelian extensions ofQ. Invent. Math.76, 179–330 (1984)
Monsky, P.: Onp-adic power series. Math. Annalen255, 217–227 (1981)
Perrin-Riou, B.: Arithmétique des courbes elliptiques et théorie d'Iwasawa. Bull. Soc. Math. France Suppl., Mémoire17 (1984)
Perrin-Riou, B.: Points de Heegner et dérivées de fonctionsL p-adiques. Invent. Math.89, 455–510 (1987)
Razar, M.: The nonvanishing ofL(1) for certain elliptic curves with no first descents. Am. J. Math.96, 104–126 (1974)
Rubin, K.: Local units, elliptic units, Heegner points and elliptic curves. Invent. Math.88, 405–422 (1987)
Rubin, K.: Global units and ideal class groups. Invent. Math.89, 511–526 (1987)
Rubin, K.: Tate-Shafarevich groups andL-functions of elliptic curves with complex multiplication. Invent. Math.89, 527–560 (1987)
Rubin, K.: On the main conjecture of Iwasawa theory for imaginary quadratic fields. Invent. Math.93, 701–713 (1988)
Rubin, K.: The Main Conjecture. Appendix to: Cyclotomic Fields I–II (Second ed.) Lang, S. (Grad. Texts in Math., vol.121, pp. 397–419). Berlin-Heidelberg-New York. Springer 1990
Rubin, K.: The one-variable main conjecture for elliptic curves with complex multiplication. To appear in the proceedings of the 1989 Durham conferenceL-functions in Arithmetic. Cambridge: Cambridge University Press (in press)
Schneps, L.: On the μ-invariants ofp-adicL-functions attached to elliptic curves with complex multiplication. J. Number Theory25, 20–33 (1987)
Shimura, G.: Introduction to the arithmetic theory of automorphic forms. Princeton: Princeton Univ. Press 1971
Tate, J.: Algorithm for determining the type of a singular fiber in an elliptic pencil. In: Modular Functions of One Variable (IV) (Lect. Notes in Math., vol.476, pp. 33–52) Berlin-Heidelberg-New York: Springer 1975
Thaine, F.: On the ideal class groups of real abelian number fields. Ann. Math.128, 1–18 (1988)
Tunnell, J.: A classical diophantine problem and modular forms of weight 3/2. Invent. Math.72, 323–334 (1983)
Wiles, A.: Higher explicit reciprocity laws. Ann. Math.107, 235–254 (1978)
Wintenberger, J-P.: Structure galoisienne de limites projectives d'unités locales. Comp. Math.42, 89–103 (1981)
Yager, R.: On two variablep-adicL-functions. Ann. Math.115, 411–449 (1982)
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Oblatum 6-II-1990
Partially supported by NSF grants
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Rubin, K. The “main conjectures” of iwasawa theory for imaginary quadratic fields. Invent Math 103, 25–68 (1991). https://doi.org/10.1007/BF01239508
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DOI: https://doi.org/10.1007/BF01239508