Commentarii Mathematici Helvetici

, Volume 59, Issue 1, pp 600–634 | Cite as

Reduction theory using semistability

  • Daniel R. Grayson


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. A. Ash, D. Mumford, M. Rapaport andY. Tai,Smooth compactification of locally symmetric varieties, Math. Sci. Press, Brookline, Mass. 1975.MATHGoogle Scholar
  2. M. F. Atiyah andR. Bott,The Yang-Mills Equations over Riemann Surfaces, Phil. Trans R. Soc., London A 308 (1982) 523.MathSciNetCrossRefGoogle Scholar
  3. R. Bieri andB. Eckmann,Groups with homological duality generalizing Poincaré duality, Inventiones Mathematicae20 (1973) 103.CrossRefMathSciNetMATHGoogle Scholar
  4. A. Borel,Reduction Theory for Arithmetic Groups, Proc. Sympos. Pure Math.9 (1966) 20, AMS, Providence, RI.Google Scholar
  5. A. Borel andJ.-P. Serre,Corners and Arithmetic Groups, Comment. Math. Helv.48 (1973) 436.CrossRefMathSciNetMATHGoogle Scholar
  6. D. Grayson,Finite Generation of K-groups of a curve over a finite field [after Daniel Quillen], Lecture Notes in Mathematics no. 966,Algebraic K-theory, Proceedings, Oberwolfach, 1980, Part I, Springer, Berlin, 1982.Google Scholar
  7. G. Harder andM. Narasimhan,On the cohomology groups of moduli spaces of vector bundles on curves, Math. Ann.212 (1975) 215.CrossRefMathSciNetMATHGoogle Scholar
  8. C. Hermite,Oeuvres, I, Paris (1905) 94.Google Scholar
  9. R. Kirby andL. Siebenmann,Foundational Essays on Topological Manifolds, Smoothing, and Triangulations, Annals of Math. Study 88, Princeton University Press, 1977.Google Scholar
  10. S. Lang,Algebraic Number Theory, Addison-Wesley, Reading, Massachusetts, 1970.MATHGoogle Scholar
  11. E. Mendoza,Cohomology of PGl 2 over imaginary Quadratic Integers, Bonner Mathematische Schriftstellen 128 (1980).Google Scholar
  12. H. Minkowski,Geometrie der Zahlen, Leipzig (1896).Google Scholar
  13. H. Minkowski,Discontinuitätsberiech fur arithmetische Äquivalenz, Ges. Werke II (1911) 53–100.Google Scholar
  14. D. Quillen,Finite generation of the groups K i of rings of algebraic integers, inAlgebraic K-theory I, Battelle Institute Conference 1972, Lecture Notes in Math. no. 341. Springer, Berling, Heidelberg, New York, 1973.Google Scholar
  15. H. Rademacher,Topics in Analytic Number Theory, Grundlehren Math. Wiss. 169, Springer, 1973.Google Scholar
  16. J-P. Serre,Arbres, Amalgames, SL 2, Astérisque no. 46, Soc. Math. France, 1977.Google Scholar
  17. J-P. Serre,Arithmetic Groups, in “Homological Group Theory”, Cambridge University Press, 1979.Google Scholar
  18. C. Siegel, Lectures on quadratic Forms, TATA, Bombay, 1957.Google Scholar
  19. U. Stuhler,Eine, Bemerkung zur Reduktionstheorie quadratischen Formen, Archiv der Math.27 (1976) 604.CrossRefMathSciNetMATHGoogle Scholar
  20. —,Zur Reduktionstheorie der positiven quadratischen Formen II, Archiv der Math.,28 (1977) 611.CrossRefMathSciNetMATHGoogle Scholar
  21. J. Tits,Buildings of spherical type and finite BN-pairs, Lecture Notes in Mathematics 386, Springer, Berlin, Heidelberg, New York, 1974.MATHGoogle Scholar
  22. A. Weil,Sur l'analogie entre les corps de nombres algébriques et les corps de fonctions algébrique [1939a], Collected Papers, vol I, Springer, 1980.Google Scholar

Copyright information

© Birkhäuser Verlag 1984

Authors and Affiliations

  • Daniel R. Grayson
    • 1
  1. 1.Dept of MathematicsUniversity of IllinoisUrbanaUSA

Personalised recommendations