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The Tate spectrum ofv n -periodic complex oriented theories

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  1. A. Adem, R. L. Cohen, and W. G. Dwyer. Generalized Tate homology, homotopy fixed points and the transfer. InContemporary Mathematics, volume 96, pages 1–13, 1989.

  2. N. A. Baas. On bordism theory of manifolds with singularities.Math. Scand., 33:279–302, 1973.

    MathSciNet  Google Scholar 

  3. A. Baker and U. Würgler. Liftings of formal groups and the Artinian completion ofv −1 n BP.Math. Proc. Cambridge Phil. Soc., 106:511–530, 1989.

    Article  MATH  Google Scholar 

  4. J.M. Boardman. Stable homotopy theory. University of Warwick, 1965.

  5. A. K. Bousfield. The Boolean algebra of spectra.Commentarii Mathematici Helvetici, 54:368–377, 1979.

    Article  MathSciNet  MATH  Google Scholar 

  6. Gunnar Carlsson. Equivariant stable homotopy and Segal’s Burnside ring conjecture.Ann. Math., 120:189–224, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  7. D. Davis, D. Johnson, J. Klippenstein, M. Mahowald, and S. Wegmann. The spectrum (P ΛBP〈2〉)_∞.Trans. Am. Math. Soc., 296:95–110, 1986.

    MathSciNet  MATH  Google Scholar 

  8. D. Davis and M. Mahowald. The spectrum (P Λbo)_∞.Math. Proc. Cam. Phil. Soc., 96:85–93, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  9. E. Devinatz, M. J. Hopkins, and J. H. Smith. Nilpotence and stable homotopy theory.Annals of Mathematics, 128:207–242, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  10. E. S. Devinatz. Small ring spectra.Journal of Pure and Applied Algebra, 81:11–16, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  11. J. P. C. Greenlees and J. P. May. Generalized Tate cohomology.Memoirs of the American Mathematical Society 543 (1995).

  12. J. H. Gunarwardena. Cohomotopy of some classifying spaces. thesis, 1981.

  13. M. J. Hopkins and J. H. Smith. Nilpotence and stable homotopy theory II. To appear.

  14. M. Hovey. Bousfield localization functors and Hopkins’ chromatic splitting conjecture. InProceedings of the Čech centennial homotopy theory conference, 1993.Contemporary Mathematics, 181:225–250, 1995.

    MathSciNet  Google Scholar 

  15. D. C. Johnson and W. S. Wilson. BP-operations and Morava’s extraordinary K-theories.Mathematische Zeitschrift, 144:55–75, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  16. L. G. Lewis, J. P. May, and M. Steinberger.Equivariant Stable Homotopy Theory, volume 1213 ofLecture Notes in Mathematics. Springer-Verlag, New York, 1986.

    Google Scholar 

  17. W. H. Lin. On conjectures of Mahowald, Segal and Sullivan.Proc. Cambridge Phil. Soc., 87:449–458, 1980.

    Article  MATH  Google Scholar 

  18. M. E. Mahowald and D. C. Ravenel. Toward a global understanding of the homotopy groups of spheres. In Samuel Gitler, editor,The Lefschetz Centennial Conference: Proceedings on Algebraic Topology, volume 58 II ofContemporary Mathematics, pages 57–74, Providence, Rhode Island, 1987. American Mathematical Society.

    Google Scholar 

  19. M. E. Mahowald and H. Sadofsky.v n -telescopes and the Adams spectral sequence.Duke Mathematical Journal, 78:101–129, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  20. M. E. Mahowald and P. Shick. Root invariants and periodicity in stable homotopy theory.Bull. London Math. Soc., 20:262–266, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  21. M.E. Mahowald and P. Shick. Periodic phenomena in the classical Adams spectral sequence.Trans. Amer. Math. Soc., 300:191–206, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  22. J.P. May Equivariant constructions of nonequivariant spectra. In W. Browder, editor,Algebraic topology and algebraic K-theory : proceedings of a conference dedicated to John C. Moore, pages 345–364, 1987. Princeton University Press.

  23. D. C. Ravenel. MoravaK-theories and finite groups. In S. Gitler, editor,Symposium on algebraic topology in honor of José Adem, Contemporary Mathematics, volume 12, pages 289–292, 1982.

  24. H. Sadofsky. The root invariant andv 1-periodic families.Topology, 31:65–111, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  25. R. Switzer.Algebraic Topology — Homotopy and Homology. Springer-Verlag, New York, 1975.

    MATH  Google Scholar 

  26. U. Würgler. Cobordism theories of unitary manifolds with singularities and formal group laws.Mathematische Zeitschrift, 150:239–260, 1976.

    Article  MathSciNet  MATH  Google Scholar 

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The second author was supported by National Science Foundation grant DMS-9107943

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Greenlees, J.P.C., Sadofsky, H. The Tate spectrum ofv n -periodic complex oriented theories. Math Z 222, 391–405 (1996).

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