Advertisement

Inventiones mathematicae

, Volume 122, Issue 1, pp 83–117 | Cite as

Zero-cycles on quadric fibrations: Finiteness theorems and the cycle map

  • R. Parimala
  • V. Suresh
Article

Keywords

Finiteness Theorem Quadric Fibrations 
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.

Unable to display preview. Download preview PDF.

References

  1. [A] Arason, J.Kr.: A proof of Merkurjev's theorem. In: Quadratic and hermitian forms, CMS Conf. Proc. Vol.4, Providence, 121–130 (1984)Google Scholar
  2. [AEJ] Arason, J.Kr., Elman, R., Jacob, B.: Fields of cohomological 2-dimension three. Math. Ann.274, 649–657 (1986)Google Scholar
  3. [AP] Arason, J.Kr., Pfister, A.: Beweis des Krullschen Durchschnittsatzes für den Wittring. Invent. Math.12, 173–176 (1971)Google Scholar
  4. [BO] Bloch, S., Ogus, A.: Gersten's conjecture and the homology of schemes. Ann. Scient. Ec. Norm. Sup. 4 Série7, 181–202 (1974)Google Scholar
  5. [CT1] Colliot-Thélène, J.-L.: Formes quadratiques multiplicatives et variété algébriques. Bull. Soc. Math. France,106, 113–151 (1978)Google Scholar
  6. [CT2] Colliot-Thélène, J.-L.: Cycles algébriques de torsion et K-théorie algébrique. In: Arithmetic algebraic geometry. Trento, SLN 1553, 1991Google Scholar
  7. [CTP] Colliot-Thélène, J.-L., Parimala, R.: Real components of algebraic varieties and étale cohomology. Invent. Math.101, 81–92 (1990)Google Scholar
  8. [CTSS] Colliot-Théléne, J.-L., Sansuc, J.-J., Swinnerton-Dyer, P.: Intersections of two quadrics and Châtelet surfaces, I.J. reine Angew. Math.373, 37–107 (1987)Google Scholar
  9. [CTS] Colliot-Thélène, J.-L., Skorobogatov, A.N.: Groupe de Chow des zérocycles sur les fibrés en quadriques. K-Theory7, 477–500 (1993)Google Scholar
  10. [CTSu] Colliot-Théléne, J.-L., Sujatha, R.: Unramified Witt groups of real anisotropic quadrics. Proc. Symp. Pure Math. Vol. 88, Part 2, p 127–147Google Scholar
  11. [G] Gros, M.: O-cycles de degré zéro sur les surface fibrées en coniques. J. reine Angew. Math.373, 166–184 (1987)Google Scholar
  12. [Grl] Grothendieck, A.: Le groupe de Brauer II, Dix exposés sur la cohomologie des schémas, pp. 67–87. Amsterdam: North-Holland 1968Google Scholar
  13. [Gr2] Grothendieck, A.: Le groupe de Brauer III, Dix exposés sur la cohomologie des schémas, pp. 88–188. Amsterdam: North-Holland 1968Google Scholar
  14. [K] Kato K.: A Hasse principle for two-dimensional global fields. J. reine Angew. Math.366, 142–181 (1986)Google Scholar
  15. [Knl] Knebusch, M.: On algebraic curves over real closed fields; II. Math. Z.151, 189–205 (1976)Google Scholar
  16. [Kn2] Knebusch, M.: Symmetric bilinear forms over algebraic varieties, Conf. on quadratic forms. Vol. 46, pp. 103–283. Kingston, Queen's papers in pure and applied math. 1977Google Scholar
  17. [Kn3] Knebusch, M.: Generic splitting of quadratic forms, I. Proc. London Math. Soc.33, 65–93 (1976)Google Scholar
  18. [L] Lam, T.Y.: The algebraic theory of quadratic forms. New York: Benjamin 1973Google Scholar
  19. [Le] Levine, M.: Zero cycles and K-theory on singular varieties, Algebraic Geometry 1985. Bowdoin, Proc. Symp. Pure Math.46 (part 2), 451–462 (1987)Google Scholar
  20. [Li] Lichtenbaum, S.: Duality theorems for curves over p-adic fields. Invent. Math.7, 120–136 (1969)Google Scholar
  21. [M] Mattuck, A.: Abelian varieties over p-adic ground fields, Ann. Math.62, 92–119 (1955)Google Scholar
  22. [Mi] Milne, J.S.: Etale Cohomology. Princeton: Princeton University Press 1980Google Scholar
  23. [P] Parimala, R.: Witt groups of curves over local fields. Comm. Algebra,17, 2857–2862 (1989)Google Scholar
  24. [Q] Quillen, D.: Higher algebraic K-theory: I. In: Algebraic K-theory I. LNM, Vol. 341, pp. 85–148 Berlin: Springer 1973Google Scholar
  25. [R] Reiner, I.: Maximal orders. London, New York, San Francisco: Academic press 1975Google Scholar
  26. [S1] Saito, S.: A conjecture of Bloch and Brauer groups of surfaces overp-adic fields. Preprint 1990Google Scholar
  27. [S2] Saito, S.: Cycle map on torsion algebraic cycles of codimension two. Invent. Math.106, 443–460 (1991)Google Scholar
  28. [Sc] Scharlau, W.: Quadratic and Hermitian forms Grundlehren der Math. Wiss., Vol. 270, Berlin, Heidelberg, New York: Springer 1985Google Scholar
  29. [Se] Serre, J.-P.: Cohomologie Galoisienne (SLN Vol. 5) Berlin, Heidelberg, New York: Springer 1963Google Scholar
  30. [Sh] Shatz, S.S.: Prifinite groups, arithmetic and geometry. Annals of Mathematics Studies, Vol. 67 Princeton: Princeton University Press 1972Google Scholar
  31. [Sk] Skorobogatov, A.N.: Arithmetic on certain quadric bundles of relative dimension two. I. J. reine Angew. Math.407, 57–74 (1990)Google Scholar
  32. [Su] Suslin, A.A.: Algebraic K-theory and the norm-residue homomorphism. J. Soviet Math.30, 2556–2611 (1985)Google Scholar
  33. [Sw] Swan, R.: K-theory of quadric hypersurfaces. Ann. Math.122, 113–153 (1985)Google Scholar
  34. [V] Van Geel, J.: Applications of the Riemann-Roch theorem for curves to quadratic forms and division algebras. Recherches de Mathématique 7, Institut de Mathématique pure et appliquée, Université Catholique de Louvain, 1991Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • R. Parimala
    • 1
  • V. Suresh
    • 1
  1. 1.Tata Institute of Fundamental ResearchSchool of MathematicsBombayIndia

Personalised recommendations