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Rigidity in motivic homotopy theory

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An Erratum to this article was published on 02 June 2011

Abstract

We show that extensions of algebraically closed fields induce full and faithful functors between the respective motivic stable homotopy categories with finite coefficients.

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References

  1. Adams, J.F.: Stable Homotopy and Generalised Homology. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL (1995). Reprint of the 1974 original

  2. Bass, H.: Algebraic K-theory. W. A. Benjamin Inc., New York, Amsterdam (1968)

    Google Scholar 

  3. Bousfield, A.K.: The localization of spectra with respect to homology. Topology 18(4), 257–281 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dundas, B.I., Röndigs, O., Østvær, P.A.: Motivic functors. Doc. Math.8, 489–525 (2003) (electronic)

  5. Fausk, H., Hu, P., May, J.P.: Isomorphisms between left and right adjoints. Theory Appl. Categ. 11(4), 107–131 (2003) (electronic)

    Google Scholar 

  6. Fulton, W.: Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol.2, 2nd edn. Springer, Berlin (1998)

  7. Goerss, P.G., Jardine, J.F.: Localization theories for simplicial presheaves. Canad. J. Math. 50(5), 1048–1089 (1998)

    MathSciNet  MATH  Google Scholar 

  8. Hasemeyer, C., Hornbostel, J.: Motives and etale motives with finite coefficients. K-Theory 34(3), 195–207 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hu, P.: On the Picard group of the stable. \({\mathbb{A}^1}\)-homotopy category Topology 44(3), 609–640 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Jardine, J.F.: Motivic symmetric spectra. Doc. Math.5, 445–553 (2000) (electronic)

    Google Scholar 

  11. Morel, F.: On the motivic π0 of the sphere spectrum. In: Axiomatic, enriched and motivic homotopy theory, NATO Sci. Ser. II Math. Phys. Chem., vol. 131, pp. 219–260. Kluwer Acad. Publ., Dordrecht (2004)

  12. Morel, F., Voevodsky, V.: A 1-homotopy theory of schemes. Inst. Hautes Études Sci. Publ. Math. 90, 45–143 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  13. Mumford, D.: Abelian varieties. Tata Institute of Fundamental Research Studies in Mathematics, No. 5. Published for the Tata Institute of Fundamental Research, Bombay (1970)

  14. Panin, I., Yagunov, S.: Rigidity for orientable functors. J. Pure Appl. Algebra 172(1), 49–77 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  15. Röndigs, O., Østvær, P.A.: Motives and modules over motivic cohomology. C. R. Math. Acad. Sci. Paris 342(10), 751–754 (2006)

    MathSciNet  MATH  Google Scholar 

  16. Suslin, A.: On the K-theory of algebraically closed fields. Invent. Math. 73(2), 241–245 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  17. Voevodsky, V.: Cancellation theorem. Preprint

  18. Voevodsky, V.: Motivic cohomology with Z/2-coefficients. Publ. Math. Inst. Hautes Études Sci. 98, 59–104 (2003)

    MathSciNet  MATH  Google Scholar 

  19. Yagunov, S.: Rigidity. II. Non-orientable case. Doc. Math.9, 29–40 (2004) (electronic)

    Google Scholar 

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Correspondence to Oliver Röndigs.

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An erratum to this article is available at http://dx.doi.org/10.1007/s00208-011-0666-z.

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Röndigs, O., Østvær, P.A. Rigidity in motivic homotopy theory. Math. Ann. 341, 651–675 (2008). https://doi.org/10.1007/s00208-008-0208-5

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  • DOI: https://doi.org/10.1007/s00208-008-0208-5

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