Inventiones mathematicae

, Volume 58, Issue 1, pp 1–35 | Cite as

Modular curves and the class group of Q(ς p )

  • Andrew Wiles
Article

Keywords

Class Group Modular Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cassels, J.W.S., Fröhlich, A.: Algebraic number theory. London-New York: Academic Press 1967Google Scholar
  2. 2.
    Coates, J.: “p-adicL-functions and Iwasawa's theory,” in Algebraic Number Fields, edited by Fröhlich, A., New York: Academic Press 1977Google Scholar
  3. 3.
    Coates, J., Lichtenbaum, S.: Onl-adic zeta functions. Ann. of Math.98, 498–550 (1973)Google Scholar
  4. 4.
    Deligne, P.: Formes modulaires et représentationsl-adiques, Séminaire Bourbaki 68/69 no. 355, Lecture Notes in Mathematics 179, 136–172, Berlin-Heidelberg-New York: Springer 1971Google Scholar
  5. 5.
    Deligne, P., Mumford, D.: The irreducibility of the space of curves of given genus. Publications Mathématiques I.H.E.S.,36, 75–109 (1969)Google Scholar
  6. 6.
    Deligne, P., Rapoport, M.: Schémas de modules de courbes elliptiques, Lecture Notes in Mathematics,349. Berlin-Heidelberg-New York: Springer 1973Google Scholar
  7. 7.
    Gras, G.: Classes d'idéaux des corps abéliens et nombres de Bernoulli généralisés. Ann. Inst. Fourier,27, 1–66 (1977)Google Scholar
  8. 8.
    Greenberg, R.: Onp-adicL-functions and cyclotomic fields. Nagoya Math. J.,56, 61–77 (1974)Google Scholar
  9. 9.
    Greenberg, R.: Onp-adicL-functions and cyclotomic fields II, Nagoya Math. J.,67, 139–158 (1977)Google Scholar
  10. 10.
    Hartshorne, R.: Residues and duality, Lecture Notes in Mathematics,20, Berlin-Heidelberg-New York: Springer 1970Google Scholar
  11. 11.
    Hartshorne, R.: Algebraic Geometry. New York-Heidelberg-Berlin: Springer 1977Google Scholar
  12. 12.
    Iwasawa, K.: On some modules in the theory of cyclotomic fields. J. Math. Soc. Japan,16, 42–82 (1964)Google Scholar
  13. 13.
    Iwasawa, K.: OnZ 1-extensions of algebraic number fields. Ann. of Math.,98, 246–326 (1973)Google Scholar
  14. 14.
    Kubert, D., Lang, S.: Thep-primary component of the cuspidal divisor class group on the modular curveX(p). Math. Ann.234, 25–44 (1978)Google Scholar
  15. 15.
    Lang, S.: Introduction to modular forms. New York-Heidelberg-Berlin: Springer 1976Google Scholar
  16. 16.
    Lang, S.: Cyclotomic fields. New York-Heidelberg-Berlin: Springer 1978Google Scholar
  17. 17.
    Mazur, B.: Modular curves and the Eisenstein ideal. Publications Mathématiques I.H.E.S.,47 (1978)Google Scholar
  18. 18.
    Mazur, B.: Rational isogenies of prime degree. Inv. Math.44, 129–162 (1978)Google Scholar
  19. 19.
    Ogg, A.: Rational points on certain elliptic modular curves. Proc. Symp. Pure Math.24, 221–231 (1973)Google Scholar
  20. 20.
    Oort, F., Tate, J.: Group schemes of prime order. Ann. Scient. Ec. Norm. Sup., série4, 3, 1–21 (1970)Google Scholar
  21. 21.
    Ribet, K.: A modular construction of unramifiedp-extensions of Q(μp). Inv. Math.,34, 151–162 (1976)Google Scholar
  22. 22.
    Serre, J.-P.: Sur la topologie des variétés algébriques en caractéristique p. Symp. Int. de Top. Alg., Mexico, 1958Google Scholar
  23. 23.
    Shimura, G.: Introduction to the arithmetic theory of automorphic forms. Publ. Math. Soc. Japan,11, Tokyo-Princeton (1971)Google Scholar
  24. 23a.
    E.G.A. III: Eléments de géométrie algébrique, by A. Grothendieck and J. Dieudonné, Publications Mathématiques I.H.E.S.,11 (1961)Google Scholar
  25. 23b.
    E.G.A. IV: Eléments de géométrie algébrique, by A. Grothendieck and J. Dieudonné, Publications Mathématiques I.H.E.S.,24 (1965)Google Scholar
  26. 23c.
    S.G.A. 5: Séminaire de géométrie algébrique du Bois-Marie, Lecture Notes in Mathematics589, Berlin-Heidelberg-New York: Springer 1977Google Scholar
  27. 23d.
    S.G.A. 7: Séminaire de géométrie algébrique du Bois-Marie, Lecture Notes in Mathematics288, Berlin-Heidelberg-New York: Springer 1972Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Andrew Wiles
    • 1
  1. 1.Dept. of MathematicsHarvard UniversityCambridgeUSA

Personalised recommendations