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Séminaire de Théorie des Nombres, Paris 1987–88 pp 155–200Cite as

Sur L’arithmétique des Corps de Nombres p-Rationnels

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Part of the book series: Progress in Mathematics ((PM,volume 81))

Abstract

Soient K un corps de nombres, de degré fini sur Q, et p un nombre premier fixé. Soient S p l’ensemble des p-places (i.e. des places au-dessus de p) de K et S un ensemble fini de places de K contenant S p . Soient K S la pro—p—extension S-ramifiée (i.e. non ramifiée en dehors de S) maximale de K, et G S = G S (K) = Gal(K S /K). L’objet essentiel de la théorie de laS-ramification, ou ratification restreinte, est l’étude du groupe de Galois G S ,dont la structure reflète les propriétés arithmétiques du corps K par rapport au nombre premier p.

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Bibliographie

  1. E. Binz, J. NeuMrch et G.H. Wenzel — A subgroup theorem for pro finite groups, J. Algebra 19 (1971), 104–109.

    Article  MathSciNet  MATH  Google Scholar 

  2. A. Frohlieh — Central extensions, Galois groups and ideal class groups of number fields, Contemporary Math. 24, AMS (1983).

    Book  Google Scholar 

  3. G. Gras — Logarithme p-adique et groupe de Galois, J. fur reine und angew. Math., 343 (1983), 64–80.

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Gras. — Remarks on K2 of number fields, J. Number Theory, 23,3 (1986), 322–335.

    Article  MathSciNet  MATH  Google Scholar 

  5. G. Gras. — Théorie des genres analytique des fonctions L p-adiques des corps totalement réels, Invent. Math. 86 (1986), 1–17.

    Article  MathSciNet  MATH  Google Scholar 

  6. G. Gras et J.—F. Jaulent.— Sur les corps de nombres réguliers, a paraitre dans Math. Zeitschrift.

    Google Scholar 

  7. H. Hasse. — Bericht Uber neuere Unterschungen und Probleme aus der Theorie der algebraischen ZahlkOrper, II, Physiea, Wiirzburg—Wien (1965).

    Google Scholar 

  8. K. Haberland. — Galois Cohomology of algebraic number fields, Deutsch. Verlag Wissen., Berlin (1978).

    Google Scholar 

  9. J.—F. Jaulent. — arithmetique des t-extensions, These d’Etat, Besangon (1986).

    Google Scholar 

  10. H. Koch.— Galoissche Theorie der p-Erweiterungen.Deutsch-Verlag Wissen, Berlin (1970)

    Google Scholar 

  11. L.V. Kuz’min. — Homology of profinite groups, Schur multipliers and class field theory, Math. USSR Izv., 3 (1969), 1149–1182.

    Article  MATH  Google Scholar 

  12. L.V. Kuz’min. — Local extensions associated with I-extensions with given ramification, Math. USSR Izv., 9 (1975), 653–726.

    Google Scholar 

  13. H. Miki. — On the Leopoldt conjecture on the p-adic regulators, J. Number Theory, 26 (1987), 117–128.

    Article  MathSciNet  MATH  Google Scholar 

  14. A. Movahhedi — Sur les p-extensions des corps p-rationnels, These Paris VII (1988).

    Google Scholar 

  15. B. Mazur and A. Wiles.— Class-fields of abelian extensions of Q, Invent. Math., 76, 2 (1984), 179–330.

    Article  MathSciNet  MATH  Google Scholar 

  16. T. Nguyen Quang Do — Formations de classes et modules d’lwasawa, dans Number Theory Noordwijkerhout 1983, Springer LNM 168 (1984), 167–185.

    Google Scholar 

  17. T. Nguyen Quang Do. — Sur la ℤp-torsion de certains modules galoisiens, Ann. Inst. Fourier, 36, 2 (1986), 27–46.

    Article  MathSciNet  MATH  Google Scholar 

  18. J. Neukirch. — Uber das Einbettungsproblem der algebraischen Zahlentheorie, Invent. Math., 21 (1973), 59–116.

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Neukirch — Freie Produkte pro-endlicher Gruppen und ihre Kohomologie, Arch. Math., 22 (1971), 337–357.

    Article  MathSciNet  MATH  Google Scholar 

  20. O. Neumann — On p-closed number fields and an analogue of Riemann’s existence theorem in algebraic number fields, dans Algebraic Number Fields, Academic Press (1977), 625–647.

    Google Scholar 

  21. J—W. Sands— Rummer’s and Iwasawa’s version of Leopoldt’s conjecture, prepublication (1986).

    Google Scholar 

  22. J.—P. Serre. — Cohomologie Galoisienne, Springer LNM5 (1965).

    MATH  Google Scholar 

  23. J. Tate - Relations between R2 and Galois cohomology, Invent. Math., 36 (1976), 257–274.

    Article  MathSciNet  MATH  Google Scholar 

  24. S.V. Ullom et S.B. Watt — Generators and relations for certain.

    Google Scholar 

  25. L.C. Washington.— Introduction to cyclotomic fields, Springer.GTM 83 (1982)

    Google Scholar 

  26. K. Wingberg. — Freie Produktzerlegungen von Galoisgruppen und Iwasawa Invarianten fûr p-Erweiterungen von Q, J. reine und angew. Math., 343 (1983), 111–129.

    Google Scholar 

  27. K. Wingberg. — On the product formula in Galois groups, J. reine und angew. Math., 368 (1986), 172–183.

    Article  MathSciNet  MATH  Google Scholar 

  28. K. Wingberg — On Galois groups of p-closed algebraic number fields with restricted ramification, prepublication (1988).

    Google Scholar 

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Author information

Authors and Affiliations

  1. UER de Mathématique—Informatique UA 212 du C.N.R.S., Universite Paris VII, 2 place Jussieu, 75251, Paris Cedex, France

    T. Nguyen Quang Do & A. Movahhedi

Authors
  1. T. Nguyen Quang Do
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  2. A. Movahhedi
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Editors and Affiliations

  1. Mathématique, Bâtiment 425, Université de Paris-Sud Centre d’Orsay, 91405, Orsay, Cédex, France

    Catherine Goldstein

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© 1990 Birkhäuser Boston

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Nguyen Quang Do, T., Movahhedi, A. (1990). Sur L’arithmétique des Corps de Nombres p-Rationnels. In: Goldstein, C. (eds) Séminaire de Théorie des Nombres, Paris 1987–88. Progress in Mathematics, vol 81. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3460-9_9

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  • DOI: https://doi.org/10.1007/978-1-4612-3460-9_9

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8032-3

  • Online ISBN: 978-1-4612-3460-9

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