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On the structure of shafarevich-tate groups

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Algebraic Geometry

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1479))

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References

  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).

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  2. Rubin, K., "The Tate-Shafarevich group and L-functions of elliptic curves with complex multiplication," Invent. Math., 89, 527–560 (1987).

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  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).

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  4. Kolyvagin, V. A., "Euler systems." To appear in the Grothendieck Festschrift, Birkhäuser.

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  5. Gross, B. H., Zagier, D., "Heegner points and derivatives of L-series," Invent. Math., 84, 225–320 (1986).

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  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).

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  7. Tate, J., "The arithmetic of elliptic curves," Invent. Math., 23, 179–206 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  8. Shimura, G., Introduction to the Arithmetic Theory of Automorphic Functions, Princeton University Press, Princeton, New Jersey (1971).

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  9. Seree, J.-P., Cohomologie Galoisienne, Springer-Verlag, Berlin-New York (1973).

    Book  Google Scholar 

  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 

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Authors and Affiliations

  1. Steklov Mathematical Institute, Vavilova St. 42, 117966, Moscow, GSP-1, Russia

    V. A. Kolyvagin

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  1. V. A. Kolyvagin
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© 1991 Springer-Verlag

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Kolyvagin, V.A. (1991). On the structure of shafarevich-tate groups. In: Algebraic Geometry. Lecture Notes in Mathematics, vol 1479. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086267

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  • DOI: https://doi.org/10.1007/BFb0086267

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54456-2

  • Online ISBN: 978-3-540-38388-8

  • eBook Packages: Springer Book Archive

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