Skip to main content

Hecke actions on Picard groups and class groups

Part II

  • 337 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 882)

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/BFb0092498
  • Chapter length: 10 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   44.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-38789-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   59.00
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. H. Bass, Algebraic K-Theory, W. A. Benjamin, New York, 1968.

    MATH  Google Scholar 

  2. N. Bourbaki, Algèbre Commutative, Chpt. I and II, Hermann, Paris, 1961.

    MATH  Google Scholar 

  3. S. Chase, D. Harrison, A. Rosenberg, Galois theory and Galois cohomology of commutative rings, Memoirs A.M.S. 52 (1965), 15–33.

    MathSciNet  MATH  Google Scholar 

  4. A. Dress, Contributions to the theory of integral, representations, Algebraic K-theory, II, edited by H. Bass, Springer Lecture Notes 342 (1973), 183–240.

    Google Scholar 

  5. J. Green, Axiomatic representation theory, J. Pure and Applied Algebra 1 (1971), 41–77.

    MathSciNet  CrossRef  MATH  Google Scholar 

  6. A. Grothendieck, Le groupe de Brauer I, II, III, pp. 46–188 in Dix exposés sur la cohomologie des schémas, edited by Grothendieck and Kuiper, North Holland, Amsterdam, 1968.

    Google Scholar 

  7. R. Hartshorne, Algebraic Geometry, GTM 52, Springer-Verlag, New York, 1977.

    MATH  Google Scholar 

  8. M. Kang, Picard groups of some rings of invariants, J of Alg. 58 (1979), 455–461.

    MathSciNet  CrossRef  MATH  Google Scholar 

  9. R. Perlis, On the class numbers of arithmetically equivalent fields, J. of Number Theory 10 Number 4 (1978), 488–509.

    MathSciNet  CrossRef  MATH  Google Scholar 

  10. P. Samuel, Lectures on unique factorization domains, Tata Inst. lecture Notes 30 (1964).

    Google Scholar 

  11. T. Suwa, The Lyndon-Hochschild-Serre spectral sequences for sheaves with operators, P.A.M.S. 77, Number 1 (1979), 32–34.

    MathSciNet  CrossRef  MATH  Google Scholar 

  12. E. Weiss, Algebraic number theory, McGarw-Hill, New York, 1963.

    MATH  Google Scholar 

  13. H. Weyl, Algebraic theory of numbers, Princeton University Press, Princeton, 1940.

    CrossRef  MATH  Google Scholar 

  14. T. Yoshida, On G-Functors (II): Hecke operators, preprint, (Dept. Math. Hokkaido University, Sappora 060, Japan).

    Google Scholar 

  15. A. Fröhlich, The Picard group of noncommutative rings, in particular of orders, Trans. A.M.S. 180 (1973), 1–45.

    MathSciNet  CrossRef  MATH  Google Scholar 

  16. A. Fröhlich, I. Reiner and S. Ulom, Picard groups and class groups of orders, Proc. L.M.S. (3) 29 (1974) 405–434.

    CrossRef  MATH  Google Scholar 

  17. I. Reiner, Class groups and Picard groups of group rings and orders, CMBS regional conference lecture notes 26, A.M.S., 1976.

    Google Scholar 

  18. H. Nehrkorn, Über absolute Idealklassengruppen und Einheiten in algebraischen Zahlkorpern, Abh. Math. Sem. Hamburg 1933, 318–334.

    Google Scholar 

  19. C. Walter, Brauer's class number relation, Acta Arith. 35 (1979), 33–40.

    MathSciNet  MATH  Google Scholar 

  20. H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, 1956.

    Google Scholar 

  21. K. Roggenkamp and L. Scott, Hecke actions on Picard groups, to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Scott, L. (1981). Hecke actions on Picard groups and class groups. In: Roggenkamp, K.W. (eds) Integral Representations and Applications. Lecture Notes in Mathematics, vol 882. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092498

Download citation

  • DOI: https://doi.org/10.1007/BFb0092498

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10880-1

  • Online ISBN: 978-3-540-38789-3

  • eBook Packages: Springer Book Archive