Skip to main content

Higher algebraic K-theory: I

Constructions

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

Keywords

  • Exact Sequence
  • Vector Bundle
  • Spectral Sequence
  • Full Subcategory
  • Canonical Isomorphism

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   49.99
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • H. Bass: Algebraic K-theory, Benjamin 1968.

    Google Scholar 

  • S. Bloch: K2 and algebraic cycles, these procedings.

    Google Scholar 

  • K. Brown and S. Gersten: Algebraic K-theory as generalized sheaf cohomology, these procedings.

    Google Scholar 

  • C. Chevalley: Les classes d'equivalence rationelle I, Exp. 2, Séminaire Chevalley 1958, Anneaux de Chow et applications, Secrétariat mathématique, Paris.

    Google Scholar 

  • A. Dold and R. Lashof: Principal quasifibrations and fibre homotopy equivalence of bundles, Ill. J. Math. 3 (1959) 285–305.

    MathSciNet  MATH  Google Scholar 

  • 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 

  • E. Friedlander: Fibrations in etale homotopy theory, Publ. Math. I.H.E.S. 42 (1972).

    Google Scholar 

  • P. Gabriel: Des categories abeliennes, Bull. Math. Soc. France 90 (1962) 323–448.

    MathSciNet  MATH  Google Scholar 

  • P. Gabriel and M. Zisman: Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35, Springer 1967.

    Google Scholar 

  • S. Gersten: The relation between the K-theory of Karoubi and Villamayor and the K-theory of Quillen (preprint).

    Google Scholar 

  • —: K-theory of regular schemes, Bull. Amer. Math. Soc. (Jan. 1973).

    Google Scholar 

  • —: On some exact sequences in the higher K-theory of rings, these procedings.

    Google Scholar 

  • —: Problems about higher K-functors, these procedings.

    Google Scholar 

  • —: Higher K-theory of rings, these procedings.

    Google Scholar 

  • A. Grothendieck: Le groupe de Brauer I, Dix exposés sur la cohomologie des schémas, North-Holland Publ. Co. 1968.

    Google Scholar 

  • A. Heller: Homological algebra in abelian categories, Ann. of Math. 68 (1958) 484–525.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • J. Milnor: The realization of a semi-simplicial complex, Ann. of Math. 65 (1957) 357–362.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • —: On spaces having the homotopy type of a CW-complex, Trans. Amer. Math. Soc. 90 (1959) 272–280.

    MathSciNet  MATH  Google Scholar 

  • D. Mumford: Lectures on curves on an algebraic surface, Annals of Math. Studies 59 (1966).

    Google Scholar 

  • 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 

  • —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 

  • —: On the endomorphism ring of a simple module over an enveloping algebra, Proc. Amer. Math. Soc. 21 (1969) 171–172.

    MathSciNet  MATH  Google Scholar 

  • L. Roberts: Real quadrics and K1 of a curve of genus zero, Mathematical Preprint No. 1971–60, Queen's University at Kingston.

    Google Scholar 

  • G. Segal: Classifying spaces and spectral sequences, Publ. Math. I.H.E.S. 34 (1968) 105–112.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • —: Categories and cohomology theories, preprint, Oxford 1972.

    Google Scholar 

  • R. G. Swan: Algebraic K-theory, Lecture notes in Math. 76 (1968).

    Google Scholar 

  • J. Tornehave: On BSG and the symmetric groups (to appear).

    Google Scholar 

  • EGA: Élements de Géométrie Algébrique, by A. Grothendieck and J. Dieudonné EGA II: Publ. Math. I.H.E.S. 8 (1961)

    Google Scholar 

  • EGA III (first part): — 11 (1961)

    Google Scholar 

  • EGA IV (third part): — 28 (1966).

    Google Scholar 

  • SGA: Séminaire de Géométrie Algébrique du Bois Marie, by A. Grothendieck and others SGA 1: Lecture Notes in Math. 224 (1971)

    Google Scholar 

  • SGA 6: — 225 (1971)

    Google Scholar 

  • SGA 2: Cohomologie locale des faisceaux cohérents et Théorèmes de Lefschetz locaux et globaux, North-Holland Publ. Co. 1968.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1973 Springer-Verlag

About this paper

Cite this paper

Quillen, D. (1973). Higher algebraic K-theory: I. In: Bass, H. (eds) Higher K-Theories. Lecture Notes in Mathematics, vol 341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067053

Download citation

  • DOI: https://doi.org/10.1007/BFb0067053

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06434-3

  • Online ISBN: 978-3-540-37767-2

  • eBook Packages: Springer Book Archive