Skip to main content
SpringerLink
Log in

Applications of algebraic K-theory to the theory of algebraic cycles

  • Conference paper
  • First Online:
Algebraic Geometry Sitges (Barcelona) 1983

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1124))

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. A. Beauville Variétés de Prym et Jacobiennes intermédiaires, Ann. Scient. Ec. Norm. Sup., 4e série, 10 (1977), p. 309–391.

    MathSciNet  MATH  Google Scholar 

  2. S. Bloch Torsion algebraic cycles and a theorem of Roitman, Comp. Math., 39, (1979), p. 107–127.

    MathSciNet  MATH  Google Scholar 

  3. S. Bloch Torsion algebraic cycles, K2, and the Brauer group of function fields, Lect. Notes in Math. No. 844, Springer Verlag, (1981), p. 75–102

    Google Scholar 

  4. S. Bloch Lectures on Algebraic cycles, Duke Univ. Math. Series IV, 1980.

    Google Scholar 

  5. S. Bloch and A. Ogus Gersten’s conjecture and the homology of schemes, Ann. Scient. Ec. Norm. Sup., 4e série, 7 (1974), p. 181–202.

    MathSciNet  MATH  Google Scholar 

  6. C. Chevalley Anneaux de Chow et applications, Séminaire Ec. Norm. Sup., (1958), Secrétariat Math. París.

    Google Scholar 

  7. W.L. Chow On equivalence classes of cycles in an algebraic variety, Ann. Math. (2), 64, (1956), p. 450–479.

    Article  MathSciNet  MATH  Google Scholar 

  8. J.L. Colliot-Thélène, J.J. Sansuc et C. Soulé Quelques théorèmes de finitude en théorie des cycles algébriques, C.R. Acad. Sc. París, 294, (1982), 749–752.

    MATH  Google Scholar 

  9. J.L. Colliot-Thélène, J.J. Sansuc et C. Soulé Torsion dans le groupe de Chow de codimension deux, Duke Math. J., 50, (1983), p.763–801.

    Article  MathSciNet  MATH  Google Scholar 

  10. P. Deligne La conjecture de Weil, I. Publ. Math. I.H.E.S. 43, (1974), 273–308

    Article  MathSciNet  MATH  Google Scholar 

  11. P. Deligne Séminaire de géomètrie algébrique du Bois-Marie SGA 41/2, Lect. Notes in Math., No. 569, Springer Verlag, (1977).

    Google Scholar 

  12. P.A. Griffiths Some transcendental methods in the study of algebraic cycles, Lect. Notes of Math., No. 185, Springer Verlag (1971), p. 1–46.

    Google Scholar 

  13. P.A. Griffiths Periods of integrals on algebraic manifolds I,II, Am. J. of Math., 90, (1968), p. 568–626, p. 805–865.

    Article  MATH  Google Scholar 

  14. P.A. Griffiths and J. Harris Principles of algebraic geometry, Wiley-Interscience, 1978

    Google Scholar 

  15. A. Grothendieck Technique de descente et théoremes d’existence en géométrie algébrique, V. Les schémas de Picard-Théorèmes d’existence. Fondaments de la Géométrie Algébrique (FGA), Sécret. Math., Paris (1962), p. 232.01–232.20.

    Google Scholar 

  16. A. Grothendieck Revêtements Etales et Groupe Fondamentale, Séminàire de géométrie algébrique du Bois-Marie SGA 1 Lect. Notes in Math., No. 224, Springer-Verlag, 1971.

    Google Scholar 

  17. R. Hartshorne Equivalence relations on algebraic cycles and subvarieties of small codimension, Proc. of Symp. in Pure Math., vol. 29, AMS, (1975), p. 129–164.

    Article  MATH  Google Scholar 

  18. R. Hartshorne, Algebraic Geometry Springer-Verlag, 1977.

    Google Scholar 

  19. W. van der Kallen Generators and relations in algebraic K-theory, Proc. ICM, Helsinki 1978, p. 305–310.

    Google Scholar 

  20. S. Lang Abelian varieties Interscience Publ., 1959.

    Google Scholar 

  21. D. Lieberman Higher Picard Varieties, Am. J. of Math., 90 (1968), p. 1165–1191.

    Article  MathSciNet  MATH  Google Scholar 

  22. D. Lieberman, Intermediate Jacobians, Algebraic Geometry Oslo 1970, Wolters-Noordhoff Publ., (1972), p. 125–139.

    Google Scholar 

  23. A.S. Merkurjev and A.A. Suslin K-cohomology of Severi-Brauer varieties and norm residue homomorphisms, Izvest. Akad. Nauk USSR, Ser. Mat. 46, (1982), p. 1011–1046. (= Math. USSR, Izvestiya, 21, (1983), 307–340).

    Google Scholar 

  24. J.S. Milne Etale Cohomology Princeton Univ. Press, 1980.

    Google Scholar 

  25. J. Milnor, Introduction to algebraic K-theory Annals of Math. Studies 72, Princeton Univ. Press, 1970.

    Google Scholar 

  26. D. Mumford Rational equivalence of zero-cycles on surfaces, J. Math. Kyoto Univ., 9, (1969), p. 195–204

    MathSciNet  MATH  Google Scholar 

  27. D. Mumford Abelian Varieties Oxford Univ. Press, 1970.

    Google Scholar 

  28. J.P. Murre Un résultat en théorie des cycles algébriques de codimension deux, C.R. Acad. Sc. Paris, 296, (1983), p. 981–984.

    MathSciNet  MATH  Google Scholar 

  29. J.P. Murre On the incidence property of the higher Picard varieties of Saito and on some related questions, Preprint.

    Google Scholar 

  30. D. Quillen, Higher algebraic K-theory I Lect. Notes of Math. No. 341 (1973), p.85–147.

    Google Scholar 

  31. A.A. Roitman, The torsion of the groups of 0-cycles modulo rational equivalence, Annals of Math., 111, (1980), p. 553–569.

    Article  MathSciNet  Google Scholar 

  32. P. Samuel Relations d’équivalence en géométrie algébrique, Proc. ICM, Edinburgh 1958, p. 470–487.

    Google Scholar 

  33. H. Saito Abelian varieties attached to cycles of intermediate dimension, Nagoya Math. J., 75, (1979), p. 95–119.

    Article  MathSciNet  MATH  Google Scholar 

  34. C. Soulé K 2 et le groupe de Brauer (d’apres Merkurjev et Suslin), Séminaire Bourbaki No. 601 (1982/83).

    Google Scholar 

  35. J. Tate, Symbols in arithmetic, Actes du Congrès Intern. des Mathématiciens, Nice 1970, Vol. 1, p. 201–212.

    MathSciNet  Google Scholar 

Download references

Authors
  1. J. P. Murre
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Eduard Casas-Alvero Gerald Welters Sebastian Xambó-Descamps

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Murre, J.P. (1985). Applications of algebraic K-theory to the theory of algebraic cycles. In: Casas-Alvero, E., Welters, G., Xambó-Descamps, S. (eds) Algebraic Geometry Sitges (Barcelona) 1983. Lecture Notes in Mathematics, vol 1124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075002

Download citation

  • DOI: https://doi.org/10.1007/BFb0075002

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15232-3

  • Online ISBN: 978-3-540-39643-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation