Skip to main content
Log in

Coates-Wiles towers in dimension two

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Arthaud, N.: On Birch and Swinnerton-Dyer's conjecture for elliptic curves with complex multiplication. I. Compos. Math.37, 209–232 (1978)

    Google Scholar 

  2. Coates, J., Wiles, A.: On the conjecture of Birch and Swinnerton-Dyer. Invent. Math.39, 223–251 (1977)

    Google Scholar 

  3. Grant, D.: Theta functions and division points on abelian varieties of dimension two. Thesis, M.I.T. 1985

  4. Gupta, R.: Ramification in the Coates-Wiles tower. Invent. Math.81, 59–69 (1985)

    Google Scholar 

  5. Hazewinkel, M.: Formal groups and applications. New York: Academic Pres 1978

    Google Scholar 

  6. Lang, S.: Elliptic curves: diophantine analysis. Berlin Heidelberg New York: Springer 1978

    Google Scholar 

  7. Lang, S.: Complex multiplication. Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  8. Lang, S.: Diophantine geometry. Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  9. Ribet, K.: Dividing rational points on abelian varieties of CM-type. Compos. Math.33, 69–74 (1976)

    Google Scholar 

  10. Rubin, K.: Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer. Invent. Math.64, 455–470 (1981)

    Google Scholar 

  11. Rubin, K.: Congruences for special values ofL-functions of elliptic curves with complex multiplication. Invent. Math.71, 339–364 (1983)

    Google Scholar 

  12. Rubin, K.: Elliptic curves andZ p -extensions. Compos. Math.56, 237–250 (1985)

    Google Scholar 

  13. Rubin, K.: Tate-Shafarevich groups andL-functions of elliptic curves with complex multiplication. Invent. Math.89, 527–560 (1987)

    Google Scholar 

  14. Rubin, K.: Global units and ideal class groups. Invent. Math.89, 511–526 (1987)

    Google Scholar 

  15. Sah, H.: Automorphisms of finite groups. J. Algebra10, 47–68 (1968)

    Google Scholar 

  16. Serre, J.-P.: Local class field theory. Algebraic number theory. Cassels, J.W.S., Fröhlich, A. (eds.) pp. 128–161, London: Academic Press 1967

    Google Scholar 

  17. Serre, J.-P.: Lie algebras and Lie groups. Reading: Benjamin 1965

    Google Scholar 

  18. Serre, J.-P., Tate, J.: Good reduction of abelian varieties. Ann. Math.88, 492–517 (1968)

    Google Scholar 

  19. Setzer, B.: The determination of all imaginary quartic, abelian number fields with class number 1. Math. Comp.35, 1383–1386 (1980)

    Google Scholar 

  20. Shimura, G.: On the zeta function of an abelian variety with complex multiplication. Ann. Math. (2)94, 504–533 (1971)

    Google Scholar 

  21. Stark, H.: The Coates-Wiles theorem revisited. Number theory related to Fermat's last theorem (Progress in Math., Vol. 26). Boston: Birkhäuser 1982

    Google Scholar 

  22. Waldschmidt, M.: Dépendance de logarithmes dans les groupes algébriques. Approximations Diophantiennes et nombres transcendants, (Progress in Math., Vol. 31). Boston: Birkhäuser 1983

    Google Scholar 

  23. Washington, L.: Introduction to cyclotomic fields. Berlin Heidelberg New York: Springer 1982

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Partially supported by NSF grant DMS 85-02804 A04

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grant, D. Coates-Wiles towers in dimension two. Math. Ann. 282, 645–666 (1988). https://doi.org/10.1007/BF01462890

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01462890

Navigation