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Part of the book series: Progress in Mathematics ((PM,volume 136))

Abstract

In this paper We will discuss an algebraic version (Theorem 1.6) of the thick subcategory theorem of Hopkins-Smith [HS] (Theorem 1.4). The former is stated as Theorem 3.4.2 in [Rav92], hut the proof given there is incorrect. (A list of errata for [Rav92] can be obtained by e-mail from the third author.)

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References

  1. J. F. Adams. Stable Homotopy and Generalised Homology. University of Chicago Press, Chicago, 1974.

    MATH  Google Scholar 

  2. 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 

  3. M. J. Hopkins and J. H. Smith. Nilpotence and stable homotopy theory II. To appear in Annals of Mathematics.

    Google Scholar 

  4. D. C. Johnson and Z. Yosimura. Torsion in Brown-Peterson homology and Hurewicz homomorphisms. Osaka Journal of Mathematics, 17:117–136, 1980.

    MathSciNet  MATH  Google Scholar 

  5. P. S. Landweber. Associated prime ideals and Hopf algebras. Journal of Pure and Applied Algebra, 3:175–179, 1973.

    MathSciNet  Google Scholar 

  6. P. S. Landweber. Homological properties of comodules over MU *(MU) and BP *(BP). American Journal of Mathematics, 98:591–610, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  7. P. S. Landweber. New applications of commutative algebra to Brown-Peterson homology. Algebraic Topology, Waterloo 1978, Lecture Notes in Mathematics 741, pages 449–460, Springer-Verlag, New York, 1979.

    Chapter  Google Scholar 

  8. S. A. Mitchell. Finite complexes with A(n)-free cohomology. Topology, 24:227–248, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  9. D. C. Ravenel. Localization with respect to certain periodic homology theories. American Journal of Mathematics, 106:351–414, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  10. D. C. Ravenel. Complex Cobordism and Stable Homotopy Groups of Spheres. Academic Press, New York, 1986.

    MATH  Google Scholar 

  11. D. C. Ravenel. Nilpotence and periodicity in stable homotopy theory. Volume 128 of Annals of Mathematics Studies, Princeton University Press, Princeton, 1992.

    Google Scholar 

  12. Yu. B. Rudyak. Exactness theorems for the cohomology theories MU, BP and P(n). Mat. Zametki, 40:115–126, 1986. English translation in Math. Notes 40:562–569, 1986.

    MathSciNet  Google Scholar 

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© 1996 Birkhäuser Verlag

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Jeanneret, A., Landweber, P.S., Ravenel, D.C. (1996). A note on the thick subcategory theorem. In: Broto, C., Casacuberta, C., Mislin, G. (eds) Algebraic Topology: New Trends in Localization and Periodicity. Progress in Mathematics, vol 136. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9018-2_14

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  • DOI: https://doi.org/10.1007/978-3-0348-9018-2_14

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9869-0

  • Online ISBN: 978-3-0348-9018-2

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