Skip to main content

The work of Mazur and Wiles on cyclotomic fields

Part of the Lecture Notes in Mathematics book series (LNM,volume 901)

This is a preview of subscription content, access via your institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. COATES, J., p-adic L-functions and Iwasawa's theory, in Algebraic Number Fields (ed. A. Fröhlich), Academic Press, (1977), 269–353.

    Google Scholar 

  2. COATES, J., SINNOTT, W., Integrality properties of the values of partial zeta functions, Proc. London Math. Soc. 34(1977), 365–384.

    MATH  MathSciNet  Google Scholar 

  3. DELIGNE, P., RAPOPORT, M., Schémas de modules de courbes elliptiques, in Springer L. N., 349(1973).

    Google Scholar 

  4. DWYER, W., FRIEDLANDER, E., Etale K-theory and arithmetic, (to appear).

    Google Scholar 

  5. GREENBERG, R., On p-adic L-functions and cyclotomic fields II, Nagoya Math. J. 67(1977), 139–158

    MATH  MathSciNet  Google Scholar 

  6. IWASAWA, K., Some modules in the theory of cyclotomic fields, J. Math. Soc. Japan 16(1964), 42–82.

    CrossRef  MATH  MathSciNet  Google Scholar 

  7. IWASAWA, K., On p-adic L-functions, Ann. of Math. 89(1969), 198–205.

    CrossRef  MATH  MathSciNet  Google Scholar 

  8. IWASAWA, K., On ℤ -extensions of algebraic number fields, Ann. of Math. 98(1973), 246–326.

    CrossRef  MATH  MathSciNet  Google Scholar 

  9. IWASAWA, K., Lectures on p-adic L-functions, Ann. Math. Studies 74, Princeton (1972).

    Google Scholar 

  10. KUBERT, D., LANG, S., The index of Stickelberger ideals of order 2 and cuspidal class numbers, Math. Ann. 237(1978), 213–232.

    CrossRef  MATH  MathSciNet  Google Scholar 

  11. KUBOTA, T., LEOPOLDT, H., Eine p-adische Theorie der zetawerte, Crelle 213(1964), 328–339.

    MathSciNet  Google Scholar 

  12. MAZUR, B., Rational isogenies of prime degree, Inventiones Math. 44(1978), 129–162.

    CrossRef  MATH  MathSciNet  Google Scholar 

  13. MAZUR, B., WILES, A., Class fields of abelian extensions of ϕ, (to appear).

    Google Scholar 

  14. NORTHCOTT, D., Finite Free Resolutions, Cambridge Tracts 71, Cambridge, 1976.

    Google Scholar 

  15. RIBET, K., A modular construction of unramified p-extensions of ϕ(μp), Inventiones Math. 34(1976), 151–162.

    CrossRef  MATH  MathSciNet  Google Scholar 

  16. SERRE, J.-P., Classes des corps cyclotomiques, Séminaire Bourbaki, exp. 174, (1958/59).

    Google Scholar 

  17. SERRE, J.-P., Formes modulaires et fonctions zêta p-adiques, in Springer L. N. 350(1973).

    Google Scholar 

  18. SHIMURA, G., Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan 11, Iwanami Shoten and Princeton (1971).

    Google Scholar 

  19. SOULÉ, C., K-théorie des anneaux d'entiers de corps de nombres et cohomologie étale, Inventiones Math. 55(1979), 251–295.

    CrossRef  MATH  Google Scholar 

  20. TATE, J., p-divisible groups, in Proceedings of a Conference on Local Fields, Springer (1967), 158–183.

    Google Scholar 

  21. WAGSTAFF, S., The irregular primes to 125000, Math. Comp. 32(1978), 583–591.

    CrossRef  MATH  MathSciNet  Google Scholar 

  22. WILES, A., Modular curves and the class group of ϕ(ζp), Inventiones Math. 58(1980), 1–35.

    CrossRef  MATH  MathSciNet  Google Scholar 

  23. LANGLANDS, R., Modular forms and ℓ-adic representations, in Springer L. N. 349(1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1981 N. Bourbaki

About this paper

Cite this paper

Coates, J. (1981). The work of Mazur and Wiles on cyclotomic fields. In: Séminaire Bourbaki vol. 1980/81 Exposés 561–578. Lecture Notes in Mathematics, vol 901. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0097200

Download citation

  • DOI: https://doi.org/10.1007/BFb0097200

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11176-4

  • Online ISBN: 978-3-540-38956-9

  • eBook Packages: Springer Book Archive