Skip to main content

Lefschetz numbers for arithmetic groups

  • Conference paper
  • First Online:
Cohomology of Arithmetic Groups and Automorphic Forms

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1447))

supported by a grant of Deutsche Forschungsgemeinschaft

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Arthur, The L 2-Lefschetz number of Hecke operators, Invent. math. 97, 1981, 257–290.

    Article  MathSciNet  Google Scholar 

  2. J. Bewersdorff, Eine Lefschetzsche Fixpunktformel für Heckeoperatoren, Bonner Mathematische Schriften Nr. 164, 1984.

    Google Scholar 

  3. K. Brown, Complete Euler characteristics and fixed-point theory, Jour. Pure and Appl. Algebra, vol. 24, 1982, 103–121.

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Borel and J.-P. Serre, Théorèmes de finitude en cohomology galoisienne, Comment. Math. Helvetici, Vol. 39, 1964, 111–196.

    Article  MathSciNet  MATH  Google Scholar 

  5. A. Borel and J. Tits, Compléments à l'article: Groupes réductifs, Pub. Math. I.H.E.S. 41, 1972, 253–276.

    Article  MathSciNet  MATH  Google Scholar 

  6. A. Borel and N. Wallach, Continuous cohomology, discrete subgroups and representations of reductive groups, Annals of Math. Studies Vol. 94, 1980, Princeton Univ. Press.

    Google Scholar 

  7. G. Harder, A Gauß-Bonnet theorem for discrete arithmetically defined groups, Ann. Scient. Éc. Norm. Sup., 4e série, 1971, 409–455.

    Google Scholar 

  8. G. Harder, On the cohomology of SL 2(O), In: Lie Groups and their Representations, Proc. of the summer school on Group Repres., London, Hilger, 1975, 139–150.

    Google Scholar 

  9. S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, London, 1962.

    MATH  Google Scholar 

  10. R. Kottwitz, Sign changes in harmonic analysis on reductive groups, Transactions A.M.S. vol. 278, 1983, 289–297.

    Article  MathSciNet  MATH  Google Scholar 

  11. R. Kottwitz, Stable trace formula, Elliptic singular terms, Math. Ann. vol. 275, 1986, 365–399.

    Article  MathSciNet  MATH  Google Scholar 

  12. R. Kottwitz, Tamagawa numbers, Ann. of Math. vol. 127, 1988, 629–646.

    Article  MathSciNet  MATH  Google Scholar 

  13. N. Krämer, Beiträge zur Arithmetik imaginär quadratischer Zahlkörper, Bonner Mathematische Schriften Nr. 161, 1985.

    Google Scholar 

  14. J.-P. Labesse, Formule des traces tordue et représentations σ-discrètes, manuscript, Paris, 1989.

    Google Scholar 

  15. Lai, K.F., Lefschetz numbers and unitary groups, preprint, Hongkong University, 1983.

    Google Scholar 

  16. Lai, K.F., Lee R., Finite group actions on Siegel modular spaces, preprint, Hongkong University, 1983.

    Google Scholar 

  17. J.-P. Labesse and J. Schwermer, On liftings and cusp cohomology of arithmetic groups, Invent. math. 83, 1986, 383–401.

    Article  MathSciNet  MATH  Google Scholar 

  18. R. Lee and J. Schwermer, The Lefschetz number of an involution on the space of cusp forms of SL 3, Invent. Math. 73, 1983, 189–239.

    Article  MathSciNet  MATH  Google Scholar 

  19. R. Lee and J. Schwermer, Geometry and arithmetic cycles attached to SL 3(ℤ) — I, Topology Vol. 25, 1986, 159–174.

    Article  MathSciNet  MATH  Google Scholar 

  20. H. Minkowski, Gesammelte Abhandlungen I, Teubner Verlag, Leipzig, Berlin, 1911.

    MATH  Google Scholar 

  21. J. Rohlfs, Arithmetisch definierte Gruppen mit Galoisoperation, Habilitations-schrift, Bonn, 1976.

    MATH  Google Scholar 

  22. J. Rohlfs, Arithmetisch definierte Gruppen mit Galoisoperation, Invent. math. 48, 1978, 185–205.

    Article  MathSciNet  MATH  Google Scholar 

  23. J. Rohlfs, The Lefschetz number of an involution on the space of classes of positive definite quadratic forms, Comment. Math. Helvetici 56, 1981, 272–296.

    Article  MathSciNet  MATH  Google Scholar 

  24. J. Rohlfs, On the cohomology of the Bianchi modular groups, Math. Z. Vol. 188, 1985, 253–269.

    Article  MathSciNet  MATH  Google Scholar 

  25. J. Rohlfs, Lefschetz numbers for arithmetic groups I, in preparation.

    Google Scholar 

  26. J. Rohlfs and B. Speh, Representations with cohomology in the discrete spectrum of subgroups of S0(n, 1)() and Lefschetz numbers, Ann. Scient. Éc. Norm. sup., 4e Série, t. 20, 1987, 89–136.

    MathSciNet  MATH  Google Scholar 

  27. J. Rohlfs and B. Speh, Automorphic representations and Lefschetz numbers, Ann. Scient. Éc. Norm. Sup. 4e série, t. 22, 1989, 473–499.

    MathSciNet  MATH  Google Scholar 

  28. J. Rohlfs and B. Speh, Boundary contributions to Lefschetz numbers for arithmetic groups I, these proceedings.

    Google Scholar 

  29. J. Rohlfs and B. Speh, Lefschetz numbers for arithmetic groups II, in preparation.

    Google Scholar 

  30. J.-P. Serre, Cohomologie Galoisienne, Lecture Notes in Math. Vol. 5, 1965, Springer Verlag, Berlin, Heidelberg, New York.

    MATH  Google Scholar 

  31. R. Steinberg, Endomorphismus of linear algebraic groups, Mem. Amer. Math. Soc. vol. 80, 1968.

    Google Scholar 

  32. J.L. Verdier, Caractéristique d'Euler-Poincaré, Bull. Soc. Math. France, t. 101, 1973, 441–445.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jean-Pierre Labesse Joachim Schwermer

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this paper

Cite this paper

Rohlfs, J. (1990). Lefschetz numbers for arithmetic groups. In: Labesse, JP., Schwermer, J. (eds) Cohomology of Arithmetic Groups and Automorphic Forms. Lecture Notes in Mathematics, vol 1447. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085735

Download citation

  • DOI: https://doi.org/10.1007/BFb0085735

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53422-8

  • Online ISBN: 978-3-540-46876-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics