Advertisement

Inventiones mathematicae

, Volume 166, Issue 1, pp 95–102 | Cite as

Rigidity for pseudo pretheories

  • Andreas Rosenschon
  • Paul Arne Østvær
Article

Abstract

Assume F is a homotopy invariant pseudo pretheory with torsion values and X is a smooth scheme of finite type over a field k. We show for certain field extensions kK the map F(X)→F(X K ) is an isomorphism.

Keywords

Line Bundle Valuation Ring Closed Subscheme Open Subscheme Smooth Scheme 
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. 1.
    Bosch, S., Lütkebohmert, W., Raynaud, M.: Néron models. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 21. Berlin: Springer 1990Google Scholar
  2. 2.
    Darnière, L.: Nonsingular Hasse principle for rings. J. Reine Angew. Math. 529, 75–100 (2000)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Friedlander, E.M., Suslin, A.: The spectral sequence relating algebraic K-theory to motivic cohomology. Ann. Sci. Éc. Norm. Supér., IV. Sér. 35, 773–875 (2002)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Green, B., Pop, F., Roquette, P.: On Rumely’s local-global principle. Jahresber. Dtsch. Math.-Ver. 97, 43–74 (1995)zbMATHGoogle Scholar
  5. 5.
    Kuhlmann, F.-V.: Dense subfields of henselian fields, and integer parts. To appear in: Proceedings of the Workshop and Conference on Logic, Algebra, and Arithmetic, Teheran, Iran, 2003Google Scholar
  6. 6.
    Panin, I., Yagunov, S.: Rigidity for orientable functors, J. Pure Appl. Algebra 172, 49–77 (2002)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Rosenschon, A., Østvær, P.A.: The homotopy limit problem for two-primary algebraic K-theory. Topology 44, 1159–1179 (2005)zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Spieß, M., Szamuely, T.: On the Albanese map for smooth quasi-projective varieties, Math. Ann. 325, 1–17 (2003)zbMATHGoogle Scholar
  9. 9.
    Suslin, A.: On the K-theory of algebraically closed fields. Invent. Math. 73, 241–245 (1983)zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Suslin, A., Voevodsky, V.: Singular homology of abstract algebraic varieties. Invent. Math. 123, 61–94 (1996)zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Voevodsky, V.: Cohomological theory of presheaves with transfers. In: Cycles, transfers, and motivic homology theories. Ann. Math. Stud., vol. 143, pp. 87–137. Princeton, NJ: Princeton Univ. Press 2000Google Scholar
  12. 12.
    Voevodsky, V.: Triangulated categories of motives over a field. In: Cycles, transfers, and motivic homology theories. Ann. Math. Stud., vol. 143, pp. 188–238. Princeton, NJ: Princeton Univ. Press 2000Google Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity at Buffalo, SUNYBuffaloUSA
  2. 2.Department of MathematicsUniversity of AlbertaEdmontonCanada
  3. 3.Department of MathematicsUniversity of OsloOsloNorway

Personalised recommendations