Skip to main content
Log in

Grothendieck and Witt groups of orders and finite groups

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Albert, A.A.: Structure of algebras. AMS Coll. Publ., 1939, rev. ed. 1961

  2. Bak, A.: On modules with quadratic forms, inK-theory and its geometric applications. Lecture Notes in Mathematics108, 55–66 (1969)

    Google Scholar 

  3. Bak. A.: The stable structure of quadratic modules, Preprint, Institute for Advanced Study, Princeton, 1970, and also a new version to appear

  4. Bak, A.: The computation of even-dimensional surgery groups of odd torsion groups (preprint)

  5. Bak, A.:K-theory of forms (preprint)

  6. Bass, H.: AlgebraicK-theory. New York: Benjamin 1968

    Google Scholar 

  7. Bass, H.: Topics in algebraick-theory. Tata Institute of Fundamental Research, Bombay, 1966

    Google Scholar 

  8. Dress, A.: Structure theorems for orthogonal representations of finite groups. To appear Bull. Am. Math. Soc. 1973.

  9. Feit, W.: Characters of finite groups. New York: Benjamin 1969

    Google Scholar 

  10. Fröhlich, A.: On theK-theory of unimodular forms over rings of algebraic integers. Quart. J. Math.22, 401–424 (1971)

    Google Scholar 

  11. Fröhlich, A., McEvett, A.M.: Forms over rings with involution. J. Algebra12, 79–104 (1969)

    Google Scholar 

  12. Knebusch, M.: Grothendieck- und Wittringe von nichtausgearteten symmetrischen Bilinearformen. S.-Ber. Heidelberger Akad. Wiss. 1969/70, 3. Abh. Berlin-Göttingen-Heidelberg: Springer 1970

    Google Scholar 

  13. Knebusch, M., Rosenberg, A., Ware, R.: Grothendieck and Witt rings of hermitian forms over Dedekind rings. To appear in Pac. J. Math.

  14. Knebusch, M., Scharlau, W.: Quadratische Formen und quadratische Reziprozitätsgesetze. Math. Z.121, 346–368 (1971)

    Google Scholar 

  15. Kneser, M.: Unpublished manuscript, 1962

  16. Landherr, W.: Liesche Ringe vom Typus A über einem algebraischen Zahlkörper und hermitesche Formen über einem Schiefkörper. Abh. Math. Sem. Hamburg12, 200–241 (1938)

    Google Scholar 

  17. Milnor, J.: Introduction to algebraicK-theory. Ann. Math. Studies 72, Princeton 1971

  18. Milnor, J., Husemoller, D.: Symmetric bilinear forms. Ergebnisse der Mathematik. Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

  19. O'Meara, O.T.: Introduction to quadratic forms. Berlin-Göttingen-Heidelberg: Springer 1963

    Google Scholar 

  20. Swan, R.:K-theory of finite groups and orders. Lecture Notes in Mathematics149, 1970

  21. Tits, J.: Forms quadratiques, groupes orthogonaux et algebres de Clifford. Inventiones math.5, 19–41 (1968)

    Google Scholar 

  22. Vaserstein, L. N.: Stabilization of unitary and orthogonal groups over a ring with involution (in Russian). Mat. Sb. (N.S.)81, (123), 328–351 (1970)

    Google Scholar 

  23. Wall, C.T.C.: On the axiomatic foundations of the theory of Hermitian forms. Proc. Camb. Phil. Soc.67, 243–250 (1970)

    Google Scholar 

  24. Wall, C.T.C.: On the classification of Hermitian forms I. Rings of algebraic integers. Comp. Math.22, 425–451 (1970)

    Google Scholar 

  25. Wall, C.T.C.: On the classification of Hermitian forms II, III, IV, V. Inventiones math.18, 119–141 (1972);19, 59–71 (1973);23, 241–260; 261–288 (1974)

    Google Scholar 

  26. Wall, C.T.C.: Surgery on compact manifolds. Academic Press, 1970

  27. Weiss, E.: Algebraic number theory. New York: McGraw-Hill 1963

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Partially supported by a National Science Foundation Grant.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bak, A., Scharlau, W. Grothendieck and Witt groups of orders and finite groups. Invent Math 23, 207–240 (1974). https://doi.org/10.1007/BF01389746

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01389746

Keywords

Navigation