References
Arthaud, N.: On Birch and Swinnerton-Dyer's conjecture for elliptic curves with complex multiplication. I. Compos. Math.37, 209–232 (1978)
Coates, J., Wiles, A.: On the conjecture of Birch and Swinnerton-Dyer. Invent. Math.39, 223–251 (1977)
Grant, D.: Theta functions and division points on abelian varieties of dimension two. Thesis, M.I.T. 1985
Gupta, R.: Ramification in the Coates-Wiles tower. Invent. Math.81, 59–69 (1985)
Hazewinkel, M.: Formal groups and applications. New York: Academic Pres 1978
Lang, S.: Elliptic curves: diophantine analysis. Berlin Heidelberg New York: Springer 1978
Lang, S.: Complex multiplication. Berlin Heidelberg New York: Springer 1983
Lang, S.: Diophantine geometry. Berlin Heidelberg New York: Springer 1983
Ribet, K.: Dividing rational points on abelian varieties of CM-type. Compos. Math.33, 69–74 (1976)
Rubin, K.: Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer. Invent. Math.64, 455–470 (1981)
Rubin, K.: Congruences for special values ofL-functions of elliptic curves with complex multiplication. Invent. Math.71, 339–364 (1983)
Rubin, K.: Elliptic curves andZ p -extensions. Compos. Math.56, 237–250 (1985)
Rubin, K.: Tate-Shafarevich groups andL-functions of elliptic curves with complex multiplication. Invent. Math.89, 527–560 (1987)
Rubin, K.: Global units and ideal class groups. Invent. Math.89, 511–526 (1987)
Sah, H.: Automorphisms of finite groups. J. Algebra10, 47–68 (1968)
Serre, J.-P.: Local class field theory. Algebraic number theory. Cassels, J.W.S., Fröhlich, A. (eds.) pp. 128–161, London: Academic Press 1967
Serre, J.-P.: Lie algebras and Lie groups. Reading: Benjamin 1965
Serre, J.-P., Tate, J.: Good reduction of abelian varieties. Ann. Math.88, 492–517 (1968)
Setzer, B.: The determination of all imaginary quartic, abelian number fields with class number 1. Math. Comp.35, 1383–1386 (1980)
Shimura, G.: On the zeta function of an abelian variety with complex multiplication. Ann. Math. (2)94, 504–533 (1971)
Stark, H.: The Coates-Wiles theorem revisited. Number theory related to Fermat's last theorem (Progress in Math., Vol. 26). Boston: Birkhäuser 1982
Waldschmidt, M.: Dépendance de logarithmes dans les groupes algébriques. Approximations Diophantiennes et nombres transcendants, (Progress in Math., Vol. 31). Boston: Birkhäuser 1983
Washington, L.: Introduction to cyclotomic fields. Berlin Heidelberg New York: Springer 1982
Author information
Authors and Affiliations
Additional information
Partially supported by NSF grant DMS 85-02804 A04
Rights 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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01462890