On the structure of shafarevich-tate groups

  • V. A. Kolyvagin
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1479)

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References

  1. 1.
    Kolyvagin, V. A., "On the Mordell-Weil group and the Shafarevich-Tate group of Weil elliptic curves," Izv. Akad. Nauk SSSR, Ser. Mat., 52, No. 6, 1154–1180 (1988).MathSciNetMATHGoogle Scholar
  2. 2.
    Rubin, K., "The Tate-Shafarevich group and L-functions of elliptic curves with complex multiplication," Invent. Math., 89, 527–560 (1987).MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Kolyvagin, V. A., "Finiteness of E(ℚ) and Ш(E, ℚ) for a subclass of Weil curves," Izv. Akad. Nauk SSSR, Ser. Mat, 52, No. 3, 522–540 (1988).MathSciNetGoogle Scholar
  4. 4.
    Kolyvagin, V. A., "Euler systems." To appear in the Grothendieck Festschrift, Birkhäuser.Google Scholar
  5. 5.
    Gross, B. H., Zagier, D., "Heegner points and derivatives of L-series," Invent. Math., 84, 225–320 (1986).MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Gross, B. H., "Kolyvagin's work on modular elliptic curves." To appear in Procedings of the Durham Symmposium on L-functions and Arithmetic (1989).Google Scholar
  7. 7.
    Tate, J., "The arithmetic of elliptic curves," Invent. Math., 23, 179–206 (1974).MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Shimura, G., Introduction to the Arithmetic Theory of Automorphic Functions, Princeton University Press, Princeton, New Jersey (1971).MATHGoogle Scholar
  9. 9.
    Seree, J.-P., Cohomologie Galoisienne, Springer-Verlag, Berlin-New York (1973).CrossRefGoogle Scholar
  10. 10.
    Kolyvagin, V. A., Logachev, D. Y., Finiteness of the Shafarevich-Tate Group and the Group of Rational Points for Some Modular Abelian Varieties, Algebra and Analysis (USSR), No. 5 (1989).Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • V. A. Kolyvagin
    • 1
  1. 1.Steklov Mathematical InstituteMoscow, GSP-1Russia

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