Skip to main content

Multiplicative galois structure

  • 919 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1068)

Keywords

  • Root Number
  • Algebraic Integer
  • Grothendieck Group
  • Torsion Class
  • Quaternion Group

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.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Artin, E. and Tate, J.: Class Field Theory. Benjamin: New York (1967).

    MATH  Google Scholar 

  2. Cassou-Nogues, Ph.: Quelques theorèmes de base normale d’entiers. Ann. Inst. Fourier 28 (1978), 1–33.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Chinburg, T.: Letter to D. Hayes, 9/15/1983.

    Google Scholar 

  4. Chinburg, T.: Multiplicative Galois Module Structure. to appear in the J. of the London Math. Soc.

    Google Scholar 

  5. Chinburg, T.: On the Galois structure of algebraic integers and S-units. Inv. Math. (in press).

    Google Scholar 

  6. Chinburg, T.: The Galois structure of S-units. to appear in the Sem. de Theorie de Nombres de Bordeaux.

    Google Scholar 

  7. Fröhlich, A.: Artin root numbers and normal integral bases for quaternion fields. Inv. Math. 17(1972), 143–166.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Frohlich, A.: Galois module structure, in “Algebraic Number Fields,” Proceedings of the Durham Symposium 1975. Academic Press: London 1977, 133–191.

    Google Scholar 

  9. Fröhlich, A.: Galois module structure of algebraic integers. Springer-Verlag: Berlin, Heidelberg, New York, Tokyo (1983).

    CrossRef  MATH  Google Scholar 

  10. Fröhlich, A.: Some problems of Galois module structure for wild extensions. Proc. London Math. Soc. 37(1978), 193–212.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Lichtenbaum, S.: Letter to J. Tate (1978).

    Google Scholar 

  12. Mazur, B. and Wiles, A.: Class fields of abelian extensions of Q. Inv. Math. (in press).

    Google Scholar 

  13. Queyrut, J.: Sommes de Gauss et structure Galoisienne des anneaux d’entiers. Sem. de Theorie de Nombres de Bordeaux, exp. 20, (1981–1982).

    Google Scholar 

  14. Queyrut, J.: Structure Galoisienne des groupes d’unites et des group des classes d’un anneau d’entiers. Sem. de Theorie de Nombres de Bordeaux, exp. 2, (1982–1983).

    Google Scholar 

  15. Serre, J. P.: Corps Locaux. 2nd ed. Paris: Hermann (1968).

    MATH  Google Scholar 

  16. Stark, H. M.: L-functions at s = 1. I, II, III, IV. Advances in Math. 7, 301–343(1971); 17, 60–92(1975); 22, 64–84(1976); 35, 197–235(1980).

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Tate, J.: Les conjectures de Stark sur les fonctions L d’Artin an s = 0; notes d’un cours a Orsay redigees par D. Bernardi et N. Schappacher. to appear.

    Google Scholar 

  18. Tate, J.: The cohomology groups of tori in finite Galois extensions of number fields. Nagoya Math. J. 27, 709–719 (1966).

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. Taylor, M. J.: On Frohlich’s conjecture for rings of integers of tame extensions. Inv. Math. 63(1981), 41–79.

    CrossRef  MATH  Google Scholar 

  20. Ullom, S. V.: A survey of class groups of integral group rings, in “Algebraic Number Fields (L-functions and Galois properties),” 709–719. New York: Academic Press (1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Chinburg, T. (1984). Multiplicative galois structure. In: Jager, H. (eds) Number Theory Noordwijkerhout 1983. Lecture Notes in Mathematics, vol 1068. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099439

Download citation

  • DOI: https://doi.org/10.1007/BFb0099439

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13356-8

  • Online ISBN: 978-3-540-38906-4

  • eBook Packages: Springer Book Archive