Skip to main content
SpringerLink
Log in

Some problems in "classical" algebraic K-theory

  • The Functors K0 And K1
  • Conference paper
  • First Online:
Book cover “Classical” Algebraic K-Theory, and Connections with Arithmetic

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 342))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S.S. Abyankhar, W. Heinzer, and P. Eakin On the uniqueness of the coefficient ring in a polynomial ring, Jour. Alg. 23 (1972) 310–342.

    Article  Google Scholar 

  2. H. BassAlgebraic K-theory, W. A. Benjamin, New York, (1968).

    Google Scholar 

  3. H. Bass Modules which support non singular forms, Jour. Alg. 13 (1969) 246–252.

    Article  MathSciNet  MATH  Google Scholar 

  4. H. Bass Projective modules over free groups are free, Jour. Alg. 1 (1964) 367–373.

    Article  MathSciNet  MATH  Google Scholar 

  5. H. Bass K-theory and stable algebra, Publ. IHES no. 22 (1964) 5–60.

    Google Scholar 

  6. H. Bass Big projective modules are free, Ill. Journ. Math., 7 (1963) 24–31.

    MathSciNet  MATH  Google Scholar 

  7. H. Bass Unitary algebraic K-theory, these Proceedings.

    Google Scholar 

  8. H. Bass, A. Heller and R.G. Swan The Whitehead group of a polynomial extension, Publ. IHES no. 22 (1964) 61–79.

    Google Scholar 

  9. H. Bass and M.P. Murthy Grothendieck groups and Picard groups of abelian group rings, Ann. Math. 86 (1967) 16–73.

    Article  MathSciNet  MATH  Google Scholar 

  10. J.W. Brewer and E.A. Rutter Isomorphic polynomial rings, Arch. Math. XXIII, (1972) 484–488.

    Article  MathSciNet  Google Scholar 

  11. A. Bialynicki-Birula Remarks on the action of an algebraic torus on kn, Bull. Acad. Polon. Sci. 14 (1966) 177–181.

    MathSciNet  Google Scholar 

  12. K.G. Chou, K.Y. Lam, and E.L.Luft On free products of rings and the coherence property, these Proceedings.

    Google Scholar 

  13. R. K. Dennis Surjective stability for K2, (to appear).

    Google Scholar 

  14. R.K. Dennis, and M. Stein, The functor K2: A survey of computations and problems, these Proceedings.

    Google Scholar 

  15. S. Endo Projective modules over polynomial rings, Jour. Math. Soc. Japan 15 (1963) 339–352.

    Article  MathSciNet  MATH  Google Scholar 

  16. D. Eisenbud and G. Evans Generating modules efficiently; theorems from algebraic K-theory, Jour. Alg. (to appear).

    Google Scholar 

  17. D. Eisenbud and G.Evans Every algebraic set in n-space is the intersection of n hypersurfaces (to appear).

    Google Scholar 

  18. D. Eisenbud and G. Evans Three conjectures about modules over polynomial rings

    Google Scholar 

  19. A. Geramita Projective modules as sums of ideals, Queen's Univ. Preprint 1969–48.

    Google Scholar 

  20. A. Geramita and L. Roberts Algebraic vector bundles on projective space, Inventiones math. 10 (1970) 298–304.

    Article  MathSciNet  MATH  Google Scholar 

  21. S. Gersten Problems about higher K-functors, these Proceedings.

    Google Scholar 

  22. S. Gersten The relationship between the K-theory of Quillen and the K-theory of Karoubi-Villamayor, (to appear).

    Google Scholar 

  23. S. Gersten Higher K-theory of rings, these Proceedings.

    Google Scholar 

  24. S. Gersten Whitehead groups of free associative algebras, Bull. Amer. Math. Soc. 71 (1965) 157–159.

    Article  MathSciNet  MATH  Google Scholar 

  25. S. Gersten On class groups of free products, Ann Math. 87 (1968) 392–398.

    Article  MathSciNet  MATH  Google Scholar 

  26. M. Hochster Nonuniqueness of coefficient rings in polynomial rings, (to appear).

    Google Scholar 

  27. G. Horrocks Projective modules over an extended local ring, Proc. Land. Math. Soc. 14 (1964) 714–718.

    Article  MathSciNet  MATH  Google Scholar 

  28. J.-P. Jouanolou Quelques calculs en K-theorie des schemes, these Proceedings.

    Google Scholar 

  29. M. Karoubi La periodicite de Bott en K-theorie generale, Ann. Sci. Ec. Norm. Sup. 4 (1971) 63–95.

    MathSciNet  MATH  Google Scholar 

  30. M. Karoubi Periodicte de la K-theorie hermitienne. Les theories6Vn etnUε, C.R. Acad. Sci. Paris t. 273 (1971) 802–805.

    MathSciNet  MATH  Google Scholar 

  31. M. Karoubi and O. Villamayor K-theorie algebrique et K-therie topologique, Math. Scand. 28 (1971) 265–307.

    MathSciNet  MATH  Google Scholar 

  32. D. Lazard, Autour de la platitude, Bull. Soc. Math. de France 97 (1969) 81–128.

    MathSciNet  MATH  Google Scholar 

  33. D. Lissner and N. Moore Projective modules over certain rings of quotients of affine rings, Jour. Alg. 15 (1970) 72–80.

    Article  MathSciNet  MATH  Google Scholar 

  34. D. Mumford Rational equivalence of 0-cycles on surface, Jour. Math. Kyoto Univ. 9 (1969) 195–204.

    MathSciNet  MATH  Google Scholar 

  35. M.P. Murthy Projective modules over a class of polynomial rings, Math. Zeit. 88 (1965) 184–189.

    Article  MathSciNet  MATH  Google Scholar 

  36. M.P. Murthy Vector bundles over affine surfaces birationally equivalent to a ruled surface, Ann. Math. 89 (1969) 242–253.

    Article  MathSciNet  MATH  Google Scholar 

  37. M.P. Murthy Projective A[x]-modules, Jour. Lond. Math. Soc. 41 (1966) 453–456.

    Article  MathSciNet  MATH  Google Scholar 

  38. M.P. Murthy Generators for certain ideals in regular rings of dimension three, (197 ) 179–184.

    Google Scholar 

  39. M.P. Murthy and C. Pedrini K0 and K1 of polynomial rings, these Proceedings.

    Google Scholar 

  40. Ojamguren and Sridharan, Cancellation of Azumaya algebras, Jour. Alg. 18 (1971) 501–505.

    Article  Google Scholar 

  41. C. Pedrini On the K0 of certain polynomial extensions, these Proceedings.

    Google Scholar 

  42. D. Quillen On the cohomology and K-theory of the general linear group over a finite field, Ann. Math (to appear).

    Google Scholar 

  43. D. Quillen Higher K-theory for categories with exact sequences, "New developments in topology," Oxford.

    Google Scholar 

  44. D. Quillen Higher Algebraic K-theory I, these Proceedings.

    Google Scholar 

  45. D. Quillen Finite generation of the groups Kn for rings of algebraic integers, these Proceedings.

    Google Scholar 

  46. C.P. Ramanujam A topological Characterisation of the affine plane as an algebraic variety, Ann. Math. 94 (1971) 69–88.

    Article  MathSciNet  MATH  Google Scholar 

  47. P. Roquette Some fundamental theorems on abelian function fields, Proc. Internat, Cong. of Math., Edinburgh (1958).

    Google Scholar 

  48. B. Segre Intersezioni complete di due ipersuperficie algebriche in uno spazio affine, et non estendibilita di un theorema di Seshadri, Rev. Roum. Math Pures et Appl. 9 (1970) 1527–1534.

    MathSciNet  Google Scholar 

  49. J.-P. Serre Faisceaux algebraiques coherents, Ann. Math. 61 (1955) 197–278.

    Article  MATH  Google Scholar 

  50. J.-P. Serre Modules projectifs et espaces fibres a fibre vectorielle, Sein Dubreil no. 23 (1957/58).

    Google Scholar 

  51. J.-P. Serre Sur les modules projectifs, Sein Dubreil no. 2 (1960/61).

    Google Scholar 

  52. C.S. Seshadri Triviality of vector bundles over the affine space K2, Proc. Natl. Acad. Sci. USA 44 (1958) 456–458.

    Article  MathSciNet  MATH  Google Scholar 

  53. P.K. Sharma and J. Strooker On a question of Swan in algebraic K-theory, (to appear).

    Google Scholar 

  54. A. Simis Projective modules of certain rings and the existence of cyclic basis, Queens Univ. Prepring no. 1970–18.

    Google Scholar 

  55. J.-P. Soublin Annueaux et modules coherents, Jour. Alg. 15 (1970) 455–472.

    Article  MathSciNet  MATH  Google Scholar 

  56. [Stal]J. Stallings Whitehead torsion of free products, Ann. Math 82 (1965) 354–363.

    Article  MathSciNet  MATH  Google Scholar 

  57. R.G. Swan Some relations between higher K-functors, Jour Alg. 21 (1972) 113–136.

    Article  MathSciNet  MATH  Google Scholar 

  58. R.G. Swan Vector bundles and projective modules, Trans, Amer. Math. Soc. (105) (1962) 264–277.

    Google Scholar 

  59. R. G. Swan Algebraic K-theory, Springer Lecture Notes 76, Berlin (1968).

    Google Scholar 

  60. J. Wagoner Buildings, stratifications, and higher K-theory, these Proceedings.

    Google Scholar 

  61. Traverso Semi-normality and Picard groups, Ann. Scuola Norm. Sup. Pisa XXIV (1970) 585–595.

    MathSciNet  Google Scholar 

  62. F. Waldhausen Whitehead groups of generalized free products, these Proceedings.

    Google Scholar 

  63. L.N. Wasserstein On the stabilisation of the general linear group over a ring, Math USSR Sbornik 8 (1969) No. 3, 383–400.

    Article  Google Scholar 

Download references

Authors
  1. Hyman Bass
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

H. Bass

Rights and permissions

Reprints and permissions

Copyright information

© 1973 Springer-Verlag

About this paper

Cite this paper

Bass, H. (1973). Some problems in "classical" algebraic K-theory. In: Bass, H. (eds) “Classical” Algebraic K-Theory, and Connections with Arithmetic. Lecture Notes in Mathematics, vol 342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073718

Download citation

  • DOI: https://doi.org/10.1007/BFb0073718

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06435-0

  • Online ISBN: 978-3-540-37770-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation