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Motivic Spaces and Spectra

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Motivic Homotopy Theory

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Abstract

As our last application of the machinery discussed in these talks, we come to an approach to the main topic of this summer school: motivic spaces and spectra.

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References

  1. 1. A. K. Bousfield and E. M. Friedlander. Homotopy theory of Ã-spaces, spectra, and bisimplicial sets. In Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977), II, Vol. 658 of Lecture Notes in Math., pp. 80–130. Springer, Berlin, 1978.

    Chapter  Google Scholar 

  2. 2. A. K. Bousfield and D. M. Kan. Homotopy limits, completions and localizations. Lecture Notes in Mathematics, Vol. 304. Springer-Verlag, Berlin, 1972.

    Google Scholar 

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

    MATH  Google Scholar 

  4. 4. W. G. Dwyer, P. S. Hirschhorn, D. M. Kan, and J. H. Smith. Homotopy limit functors on model categories and homotopical categories, Vol. 113 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2004.

    MATH  Google Scholar 

  5. 5. A. D. Elmendorf, I. Kriz, M. A. Mandell, and J. P. May. Rings, modules, and algebras in stable homotopy theory, Vol. 47 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 1997. With an appendix by M. Cole.

    MATH  Google Scholar 

  6. 6. P. G. Goerss and J. F. Jardine. Simplicial homotopy theory, Vol. 174 of Progress in Mathematics. Birkhäuser Verlag, Basel, 1999.

    MATH  Google Scholar 

  7. 7. A. Hatcher. Algebraic topology. Cambridge University Press, Cambridge, 2002.

    MATH  Google Scholar 

  8. 8. P. S. Hirschhorn. Model categories and their localizations, Vol. 99 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2003.

    MATH  Google Scholar 

  9. 9. M. Hovey. Model categories, Vol. 63 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 1999.

    MATH  Google Scholar 

  10. 10. M. Hovey. Spectra and symmetric spectra in general model categories. J. Pure Appl. Algebra, 165(1): 63–127, 2001.

    Article  MATH  Google Scholar 

  11. 11. M. Hovey, B. Shipley, and J. Smith. Symmetric spectra. J. Amer. Math. Soc., 3(1): 149–208, 2000.

    Article  Google Scholar 

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

    MATH  Google Scholar 

  13. 13. M. Levine. Lectures in nordfjordeid. In Summer school on motivic homotopy theory. This volume.

    Google Scholar 

  14. 14. E. L. Lima. The Spanier-Whitehead duality in new homotopy categories. Summa Brasil. Math., 4: 91–148, 1959.

    Google Scholar 

  15. 15. M. Lydakis. Simplicial functors and stable homotopy theory. Preprint 98-049, SFB 343, Bielefeld, June 1998.

    Google Scholar 

  16. 16. S. M. Lane. Categories for the working mathematician, Vol. 5 of Graduate Texts in Mathematics. Springer-Verlag, New York, second edition, 1998.

    Google Scholar 

  17. 17. J. Peter May. Simplicial objects in algebraic topology. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 1992. Reprint of the 1967 original.

    MATH  Google Scholar 

  18. 18. J. R. Munkres. Topology: a first course. Prentice-Hall Inc., Englewood Cliffs, N.J., 1975.

    MATH  Google Scholar 

  19. 19. D. Quillen. Rational homotopy theory. Ann. of Math. (2), 90: 205–295, 1969.

    Article  Google Scholar 

  20. 20. D. Quillen. On the (co-)homology of commutative rings. In Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVII, New York, 1968), pp. 65–87. Amer. Math. Soc., Providence, R.I., 1970.

    Google Scholar 

  21. 21. D. G. Quillen. Homotopical algebra. Lecture Notes in Mathematics, No. 43. Springer-Verlag, Berlin, 1967.

    MATH  Google Scholar 

  22. 22. V. Voevodsky, P. A. Østvær, and O. Röndigs. Voevodsky's lectures in nordfjordeid. In Summer school on motivic homotopy theory. This volume.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, Bergen, 5008, Norway

    Bjørn Ian Dundas

Authors
  1. Bjørn Ian Dundas
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Oslo, 0316, 1053, Blindern, Oslo, Norway

    Bjørn Ian Dundas

  2. Department of Mathematics, Northeastern University, 360 Huntington Avenue, 02115, Boston, MA, USA

    Marc Levine

  3. Department of Mathematics, University of Oslo, 0316, 1053, Blindern, Oslo, Norway

    Paul Arne Østvær

  4. Fakultät für Mathematik, Universität Bielefeld, 33501, 100 131, Bielefeld, Germany

    Oliver Röndigs

  5. School of Mathematics, Princeton University, 08540, Princeton, NJ, USA

    Vladimir Voevodsky

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Dundas, B.I. (2007). Motivic Spaces and Spectra. In: Dundas, B.I., Levine, M., Østvær, P.A., Röndigs, O., Voevodsky, V. (eds) Motivic Homotopy Theory. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45897-5_4

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