Skip to main content

Galois descent and class groups of orders

Part of the Lecture Notes in Mathematics book series (LNM,volume 1142)

Keywords

  • Commutative Diagram
  • Finite Type
  • Galois Extension
  • Linear Algebraic Group
  • Chow 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. H. Bass: Algebraic K-theory, Benjamin, New York 1968

    MATH  Google Scholar 

  2. S. Bloch: Torsion algebraic cycles, K2 and Brauer groups of function fields, in Lecture Notes in Mathematics 844, Springer-Verlag, Berlin-Heidelberg-New York 1981

    MATH  Google Scholar 

  3. S. Bloch: On the Chow groups of certain rational surfaces, Ann. Scient. Éc. Norm. Sup. 14 (1981), 1–23

    MathSciNet  MATH  Google Scholar 

  4. A. Borel: Linear Algebraic Groups, Benjamin, New York 1969

    MATH  Google Scholar 

  5. J.-L. Colliot-Thélène, J.-J. Sansuc: On the Chow groups of certain rational surfaces: a sequel to a paper of S. Bloch, Duke Math. J. 48 (1981), 421–447

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. J.-L. Colliot-Thélène, J.-J. Sansuc: Quelques gammes sur les formes quadratiques, J. Algebra 84 (1983), 449–467

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. J.-L. Colliot-Thélène, J.-J. Sansuc, H.P.F. Swinnerton-Dyer: Intersections de deux quadriques et surfaces de Chatelet, C.R. Acad. Sc. Paris 298 (1984), 377–380

    MathSciNet  MATH  Google Scholar 

  8. C.W. Curtis-I. Reiner: Methods of Representation Theory vol 1, Wiley (Inter-science), New York 1981

    MATH  Google Scholar 

  9. P.K. Draxl: Skew fields, London Math. Soc. Lecture Note Series 81, Cambridge University Press, Cambridge 1983

    CrossRef  MATH  Google Scholar 

  10. R. Fossum: The Divisor Class Group of a Krull domain, Springer-Verlag, Berlin-Heidelberg-New York 1973

    CrossRef  MATH  Google Scholar 

  11. H. Gillet: Rieman-Roch theorems for higher algebraic K-theory, Adv. in Math. 40 (1981), 203–289

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. A. Grothendieck: Le groupe de Brauer III, in Dix exposés sur la cohomologie des schémas, North-Holland Pub., Amsterdam 1968

    Google Scholar 

  13. A. Grothendieck, J. Dieudonné: Eléments de géométrie algébrique IV (Seconde partie), Pub. Math. Inst. Hautes Etudes Sci. No. 24 (1965)

    Google Scholar 

  14. B. Iversen: Generic Local Structure in Commutative Algebra, Lecture Notes in Mathematics 31, Springer-Verlag, Berlin-Heidelberg-New York 1973

    CrossRef  MATH  Google Scholar 

  15. I. Kaplansky: Commutative rings, Queen Mary College Notes, 1966

    Google Scholar 

  16. K. Kato: Galois cohomology of complete discrete valuation fields, in Lecture Notes in Mathematics 967, Springer-Verlag, Berlin-Heidelberg-New York 1982

    MATH  Google Scholar 

  17. M.E. Keating: On the K-theory of tiled orders, J. Algebra 43 (1976), 193–197

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. M.E. Keating: The K-theory of triangular rings and orders, in Lecture Notes in Mathematics 1046, Springer-Verlag, Berlin-Heidelberg-New York 1984

    MATH  Google Scholar 

  19. M.-A. Knus, M. Ojanguren: Théorie de la Descente et Algèbres d’Azumaya, Lecture Notes in Mathematics 389, Springer-Verlag, Berlin-Heidelberg-New York 1974

    CrossRef  MATH  Google Scholar 

  20. S. Lang: Fundamentals of Diophantine Geometry, Springer-Verlag, Berlin-Heidelberg-New York 1983

    CrossRef  MATH  Google Scholar 

  21. J.L. Loday: K-theorie algébrique et représentations des groupes, Ann. Scient. Éc. Norm. Sup. 9 (1976), 309–377

    MathSciNet  MATH  Google Scholar 

  22. A.S. Merkur’ev, A.A. Suslin: K-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Izvestija Akad. Nauk SSSR Ser. Mat. Tom 46 no 5 (1982), 1011–1046 (engl. transl.: Math. USSR Izvestija 21 (1983) No 2, 307–340)

    MathSciNet  MATH  Google Scholar 

  23. D. Quillen: Higher algebraic K-theory I, in Lecture Notes in Mathematics 341, Springer-Verlag, Berlin-Hedelberg-New York 1973

    MATH  Google Scholar 

  24. I. Reiner: Maximal orders, Academic Press, London 1975

    MATH  Google Scholar 

  25. P. Salberger: On Chow groups of conic bundle surfaces (preprint)

    Google Scholar 

  26. J.-P. Serre: Corps locaux (2 ème éd), Hermann, Paris 1968

    Google Scholar 

  27. S. Shatz: Profinite Groups, Arithmetic and Geometry, Annals of Math. Studies 67, Princeton University Press, Princeton 1972

    CrossRef  MATH  Google Scholar 

  28. R.G. Swan: Strong approximation and locally free modules, in Ring Theory and Algebra III, ed. B. Mc Donald, New York 1980

    Google Scholar 

  29. R.G. Swan: Projective modules over binary polyhedral groups, J. Reine angew. Math. 342 (1983), 66–172

    MathSciNet  MATH  Google Scholar 

  30. J. Tate: Duality theorems in Galois cohomology over number fields, in Proc. Int. Congress, Stockholm 1962

    Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  32. V.E. Voskresenskii: Birational properties of linear algebraic groups, Izvestija. Akad. Nauk SSSR Ser. Mat. 34 (1970), 3–19 (engl. transl.: Math. USSR Izvestija 4 (1970), 1–17)

    MathSciNet  Google Scholar 

  33. J. Wagoner: Delooping classifying spaces in algebraic K-theory, Topology 11 (1972), 349–370

    CrossRef  MathSciNet  MATH  Google Scholar 

  34. E. Witt: Riemann-Rochscher Satz und Z-Funktionen im Hyperkomplexen, Math. Ann. 110 (1934), 12–28

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Salberger, P. (1985). Galois descent and class groups of orders. In: Reiner, I., Roggenkamp, K.W. (eds) Orders and their Applications. Lecture Notes in Mathematics, vol 1142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074805

Download citation

  • DOI: https://doi.org/10.1007/BFb0074805

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15674-1

  • Online ISBN: 978-3-540-39601-7

  • eBook Packages: Springer Book Archive