Higher K-Theories pp 85-147 | Cite as
Higher algebraic K-theory: I
Constructions
First Online:
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.
Preview
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.MathSciNetzbMATHGoogle 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.MathSciNetzbMATHGoogle 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.MathSciNetCrossRefzbMATHGoogle Scholar
- J. Milnor: The realization of a semi-simplicial complex, Ann. of Math. 65 (1957) 357–362.MathSciNetCrossRefzbMATHGoogle Scholar
- —: On spaces having the homotopy type of a CW-complex, Trans. Amer. Math. Soc. 90 (1959) 272–280.MathSciNetzbMATHGoogle 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.MathSciNetzbMATHGoogle 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.MathSciNetCrossRefzbMATHGoogle 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
Copyright information
© Springer-Verlag 1973