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Reduction theory using semistability

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Commentarii Mathematici Helvetici

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References

  • A. Ash, D. Mumford, M. Rapaport andY. Tai,Smooth compactification of locally symmetric varieties, Math. Sci. Press, Brookline, Mass. 1975.

    MATH  Google Scholar 

  • M. F. Atiyah andR. Bott,The Yang-Mills Equations over Riemann Surfaces, Phil. Trans R. Soc., London A 308 (1982) 523.

    Article  MathSciNet  Google Scholar 

  • R. Bieri andB. Eckmann,Groups with homological duality generalizing Poincaré duality, Inventiones Mathematicae20 (1973) 103.

    Article  MathSciNet  MATH  Google Scholar 

  • A. Borel,Reduction Theory for Arithmetic Groups, Proc. Sympos. Pure Math.9 (1966) 20, AMS, Providence, RI.

    Google Scholar 

  • A. Borel andJ.-P. Serre,Corners and Arithmetic Groups, Comment. Math. Helv.48 (1973) 436.

    Article  MathSciNet  MATH  Google Scholar 

  • 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 

  • G. Harder andM. Narasimhan,On the cohomology groups of moduli spaces of vector bundles on curves, Math. Ann.212 (1975) 215.

    Article  MathSciNet  MATH  Google Scholar 

  • C. Hermite,Oeuvres, I, Paris (1905) 94.

  • R. Kirby andL. Siebenmann,Foundational Essays on Topological Manifolds, Smoothing, and Triangulations, Annals of Math. Study 88, Princeton University Press, 1977.

  • S. Lang,Algebraic Number Theory, Addison-Wesley, Reading, Massachusetts, 1970.

    MATH  Google Scholar 

  • E. Mendoza,Cohomology of PGl 2 over imaginary Quadratic Integers, Bonner Mathematische Schriftstellen 128 (1980).

  • H. Minkowski,Geometrie der Zahlen, Leipzig (1896).

  • H. Minkowski,Discontinuitätsberiech fur arithmetische Äquivalenz, Ges. Werke II (1911) 53–100.

    Google Scholar 

  • 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 

  • H. Rademacher,Topics in Analytic Number Theory, Grundlehren Math. Wiss. 169, Springer, 1973.

  • J-P. Serre,Arbres, Amalgames, SL 2, Astérisque no. 46, Soc. Math. France, 1977.

  • J-P. Serre,Arithmetic Groups, in “Homological Group Theory”, Cambridge University Press, 1979.

  • C. Siegel, Lectures on quadratic Forms, TATA, Bombay, 1957.

    Google Scholar 

  • U. Stuhler,Eine, Bemerkung zur Reduktionstheorie quadratischen Formen, Archiv der Math.27 (1976) 604.

    Article  MathSciNet  MATH  Google Scholar 

  • —,Zur Reduktionstheorie der positiven quadratischen Formen II, Archiv der Math.,28 (1977) 611.

    Article  MathSciNet  MATH  Google Scholar 

  • J. Tits,Buildings of spherical type and finite BN-pairs, Lecture Notes in Mathematics 386, Springer, Berlin, Heidelberg, New York, 1974.

    MATH  Google Scholar 

  • A. Weil,Sur l'analogie entre les corps de nombres algébriques et les corps de fonctions algébrique [1939a], Collected Papers, vol I, Springer, 1980.

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This research was supported by the National Science Foundation through the Institute for Advanced Study and the University of Illinois.

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Grayson, D.R. Reduction theory using semistability. Commentarii Mathematici Helvetici 59, 600–634 (1984). https://doi.org/10.1007/BF02566369

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  • DOI: https://doi.org/10.1007/BF02566369

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