Higher algebraic K-theory: I

  • Daniel Quillen
Part of the Lecture Notes in Mathematics book series (LNM, volume 341)


Exact Sequence Vector Bundle Spectral Sequence Full Subcategory Canonical Isomorphism 
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  1. H. Bass: Algebraic K-theory, Benjamin 1968.Google Scholar
  2. S. Bloch: K2 and algebraic cycles, these procedings.Google Scholar
  3. K. Brown and S. Gersten: Algebraic K-theory as generalized sheaf cohomology, these procedings.Google Scholar
  4. C. Chevalley: Les classes d'equivalence rationelle I, Exp. 2, Séminaire Chevalley 1958, Anneaux de Chow et applications, Secrétariat mathématique, Paris.Google Scholar
  5. A. Dold and R. Lashof: Principal quasifibrations and fibre homotopy equivalence of bundles, Ill. J. Math. 3 (1959) 285–305.MathSciNetzbMATHGoogle Scholar
  6. F. T. Farrell and W. C. Hsiang: A formula for K1Rα[T], Applications of categorical algebra, Procedings of symposia in pure mathematics XVIII (1970), Amer. Math. Soc.Google Scholar
  7. E. Friedlander: Fibrations in etale homotopy theory, Publ. Math. I.H.E.S. 42 (1972).Google Scholar
  8. P. Gabriel: Des categories abeliennes, Bull. Math. Soc. France 90 (1962) 323–448.MathSciNetzbMATHGoogle Scholar
  9. P. Gabriel and M. Zisman: Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35, Springer 1967.Google Scholar
  10. S. Gersten: The relation between the K-theory of Karoubi and Villamayor and the K-theory of Quillen (preprint).Google Scholar
  11. —: K-theory of regular schemes, Bull. Amer. Math. Soc. (Jan. 1973).Google Scholar
  12. —: On some exact sequences in the higher K-theory of rings, these procedings.Google Scholar
  13. —: Problems about higher K-functors, these procedings.Google Scholar
  14. —: Higher K-theory of rings, these procedings.Google Scholar
  15. A. Grothendieck: Le groupe de Brauer I, Dix exposés sur la cohomologie des schémas, North-Holland Publ. Co. 1968.Google Scholar
  16. A. Heller: Homological algebra in abelian categories, Ann. of Math. 68 (1958) 484–525.MathSciNetCrossRefzbMATHGoogle Scholar
  17. J. Milnor: The realization of a semi-simplicial complex, Ann. of Math. 65 (1957) 357–362.MathSciNetCrossRefzbMATHGoogle Scholar
  18. —: On spaces having the homotopy type of a CW-complex, Trans. Amer. Math. Soc. 90 (1959) 272–280.MathSciNetzbMATHGoogle Scholar
  19. D. Mumford: Lectures on curves on an algebraic surface, Annals of Math. Studies 59 (1966).Google Scholar
  20. D. Quillen 1: Higher K-theory for categories with exact sequences, to appear in the procedings of the June 1972 Oxford symposium "New developments in topology".Google Scholar
  21. —D. Quillen: On the cohomology and K-theory of the general linear groups over a finite field, Ann. of Math. 96 (1972) 552-586.Google Scholar
  22. —: On the endomorphism ring of a simple module over an enveloping algebra, Proc. Amer. Math. Soc. 21 (1969) 171–172.MathSciNetzbMATHGoogle Scholar
  23. L. Roberts: Real quadrics and K1 of a curve of genus zero, Mathematical Preprint No. 1971–60, Queen's University at Kingston.Google Scholar
  24. G. Segal: Classifying spaces and spectral sequences, Publ. Math. I.H.E.S. 34 (1968) 105–112.MathSciNetCrossRefzbMATHGoogle Scholar
  25. —: Categories and cohomology theories, preprint, Oxford 1972.Google Scholar
  26. R. G. Swan: Algebraic K-theory, Lecture notes in Math. 76 (1968).Google Scholar
  27. J. Tornehave: On BSG and the symmetric groups (to appear).Google Scholar
  28. EGA: Élements de Géométrie Algébrique, by A. Grothendieck and J. Dieudonné EGA II: Publ. Math. I.H.E.S. 8 (1961)Google Scholar
  29. EGA III (first part): — 11 (1961)Google Scholar
  30. EGA IV (third part): — 28 (1966).Google Scholar
  31. SGA: Séminaire de Géométrie Algébrique du Bois Marie, by A. Grothendieck and others SGA 1: Lecture Notes in Math. 224 (1971)Google Scholar
  32. SGA 6: — 225 (1971)Google Scholar
  33. SGA 2: Cohomologie locale des faisceaux cohérents et Théorèmes de Lefschetz locaux et globaux, North-Holland Publ. Co. 1968.Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Daniel Quillen
    • 1
  1. 1.Massachusetts Institute of TechnologyUSA

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