The work of Mazur and Wiles on cyclotomic fields

John Coates

Séminaire Bourbaki (1980-1981)

  • Volume: 23, page 220-242
  • ISSN: 0303-1179

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Coates, John. "The work of Mazur and Wiles on cyclotomic fields." Séminaire Bourbaki 23 (1980-1981): 220-242. <http://eudml.org/doc/109974>.

@article{Coates1980-1981,
author = {Coates, John},
journal = {Séminaire Bourbaki},
keywords = {cyclotomic fields; ideal class group; characteristic power series; Iwasawa's main conjecture; unramified extensions; Mazur and Wiles' main theorem; p-adic L-function},
language = {eng},
pages = {220-242},
publisher = {Springer-Verlag},
title = {The work of Mazur and Wiles on cyclotomic fields},
url = {http://eudml.org/doc/109974},
volume = {23},
year = {1980-1981},
}

TY - JOUR
AU - Coates, John
TI - The work of Mazur and Wiles on cyclotomic fields
JO - Séminaire Bourbaki
PY - 1980-1981
PB - Springer-Verlag
VL - 23
SP - 220
EP - 242
LA - eng
KW - cyclotomic fields; ideal class group; characteristic power series; Iwasawa's main conjecture; unramified extensions; Mazur and Wiles' main theorem; p-adic L-function
UR - http://eudml.org/doc/109974
ER -

References

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  1. [1] Coates, J., p-adic L-functions and Iwasawa's theory, in Algebraic Number Fields (ed. A. Fröhlich), Academic Press, (1977), 269-353. Zbl0393.12027MR460282
  2. [2] Coates, J., Sinnott, W., Integrality properties of the values of partial zeta functions, Proc. London Math. Soc.34(1977), 365-384. Zbl0354.12009MR439815
  3. [3] Deligne, P., Rapoport, M., Schémas de modules de courbes elliptiques, in Springer L. N., 349(1973). Zbl0281.14010MR337993
  4. [4] Dwyer, W., Friedlander, E., Etale K-theory and arithmetic, (to appear). Zbl0494.18009MR648533
  5. [5] Greenberg, R., On p-adic L-functions and cyclotomic fields II, Nagoya Math. J.67(1977), 139-158 Zbl0373.12007MR444614
  6. [6] Iwasawa, K., Some modules in the theory of cyclotomic fields, J. Math. Soc. Japan16(1964), 42-82. Zbl0125.29207MR215811
  7. [7] Iwasawa, K., On p-adic L-functions, Ann. of Math.89(1969), 198-205. Zbl0186.09201MR269627
  8. [8] Iwasawa, K., On Zl-extensions of algebraic number fields, Ann. of Math.98(1973), 246-326. Zbl0285.12008MR349627
  9. [9] Iwasawa, K., Lectures on p-adic L-functions, Ann. Math. Studies74, Princeton (1972). Zbl0236.12001MR360526
  10. [10] Kubert, D., Lang, S., The index of Stickelberger ideals of order 2 and cuspidal class numbers, Math. Ann.237(1978), 213-232. Zbl0371.12023MR508753
  11. [11] Kubota, T., Leopoldt, H., Eine p-adische Theorie der zetawerte, Crelle213(1964), 328-339. Zbl0186.09103
  12. [12] Mazur, B., Rational isogenies of prime degree, Inventiones Math.44(1978), 129-162. Zbl0386.14009MR482230
  13. [13] Mazur, B., Wiles, A., Class fields of abelian extensions of Q , (to appear). Zbl0545.12005MR742853
  14. [14] Northcott, D., Finite Free Resolutions, Cambridge Tracts71, Cambridge, 1976. Zbl0328.13010MR460383
  15. [15] Ribet, K., A modular construction of unramified p-extensions of Q(μp) , Inventiones Math.34(1976), 151-162. Zbl0338.12003
  16. [16] Serre, J.-P., Classes des corps cyclotomiques, Séminaire Bourbaki, exp. 174, (1958/59). Zbl0119.27603
  17. [17] Serre, J.-P., Formes modulaires et fonctions zêta p-adiques, in Springer L. N.350(1973). Zbl0277.12014MR404145
  18. [18] Shimura, G., Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan11, IwanamiShoten and Princeton (1971). Zbl0221.10029MR314766
  19. [19] Soulé, C., K-théorie des anneaux d'entiers de corps de nombres et cohomologie étale, Inventiones Math.55(1979), 251-295. Zbl0437.12008MR553999
  20. [20] Tate, J., p-divisible groups, in Proceedings of a Conference on Local Fields, Springer (1967), 158-183. Zbl0157.27601MR231827
  21. [21] Wagstaff, S., The irregular primes to 125000 , Math. Comp.32(1978), 583-591. Zbl0377.10002MR491465
  22. [22] Wiles, A., Modular curves and the class group of Q(ζp) , Inventiones Math.58(1980), 1-35. Zbl0436.12004
  23. [23] Langlands, R., Modular forms and l-adic representations, in Springer L. N.349(1973). Zbl0279.14007MR354617

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