Skip to main content
Log in

Zero-cycles on rational surfaces over number fields

  • Published:
Inventiones mathematicae Aims and scope

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Bloch, S.: On the Chow groups of certain rational surfaces. Ann. Sci. Ec. Norm. Super.14, 41–59 (1981)

    Google Scholar 

  2. Colliot-Thélène J.-L., Coray, D.: L'équivalence rationnelle sur les points fermés des surfaces rationnelles fibrées en coniques. Compos. Math.39, 301–332 (1979)

    Google Scholar 

  3. Colliot-Thélène, J.-L., Ischebeck, F.: L'équivalence rationnelle sur les cycles de dimension zéro des variétés algébriques réelles. C.R. Acad. Sci. Paris, Sér. I. Math.292, 723–725 (1981)

    Google Scholar 

  4. Colliot-Thélène, J.-L., Sansuc, J.-J.: La descente sur les variétés rationnelles. In: Journées de Géométrie algébrique d'Angers (1979), pp. 223–237, Sijthoff & Noordhoff, Alphen aan den Rijn 1980

    Google Scholar 

  5. Colliot-Thélène, J.-L., Sansuc, J.-J.: On the Chow groups of certain rational surfaces: a sequel to a paper of S. Bloch. Duke Math. J.48, 421–447 (1981)

    Google Scholar 

  6. Colliot-Thélène, J.-L., Sansuc, J.-J., Sir Peter Swinnerton-Dyer: Intersections of two quadrics and Châtelet surfaces. J. Reine Angew. Math.373, 37–107 (1987) and334, 72–168 (1987)

    Google Scholar 

  7. Kunyavskii, B.È., Skorobogatov, A.N., Tsfasman, M.A.: Combinatorics and geometry of Del Pezzo surfaces of degree 4. Russ. Math. Surv.40:6, 131–132 (1985) (see also “Del Pezzo Surfaces of degree 4”, to appear in Mémoires de la Soc. Math. Fr.)

    Google Scholar 

  8. Lang, S.: Algebraic number theory. Reading: Addison-Wesley 1970

    Google Scholar 

  9. Salberger, P.:K-theory of orders and their Brauer-Severi schemes. Thesis, Department of Mathematics, University of Göteborg 1985

  10. Salberger, P.: On the arithmetic of conic bundle surfaces. Séminaire de Théorie des nombres, Paris 1985–86, Progr. Math.71, Basel Boston: Birkhäuser 1987

    Google Scholar 

  11. Sansuc, J.-J.: Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres. J. Reine Angew. Math.327, 12–80 (1981)

    Google Scholar 

  12. Sansuc, J.-J.: Descente et principe de Hasse pour certaines variétés rationnelles. Séminaire de Théorie des Nombres, Paris 1980–81. Progr. Math. 22. Basel Boston: Birkhäuser 1982

    Google Scholar 

  13. Sansuc, J.-J.: A propos d'une conjecture arithmétique sur le groupe de Chow d'une surface rationnelle, Séminaire de Théorie des Nombres, Bordeaux 1981–82

  14. Tate, J.T.: The cohomology groups of tori in finite Galois extensions of number fields. Nagoya Math. J.27, 709–719 (1966)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research supported by the Swedish Natural Science Research Council

Rights and permissions

Reprints and permissions

About this article

Cite this article

Salberger, P. Zero-cycles on rational surfaces over number fields. Invent Math 91, 505–524 (1988). https://doi.org/10.1007/BF01388784

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01388784

Keywords

Navigation