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Inventiones mathematicae

, Volume 139, Issue 1, pp 99–133 | Cite as

Smashing subcategories and the telescope conjecture – an algebraic approach

  • Henning Krause
Article

Abstract.

We prove a modified version of Ravenel’s telescope conjecture. It is shown that every smashing subcategory of the stable homotopy category is generated by a set of maps between finite spectra. This result is based on a new characterization of smashing subcategories, which leads in addition to a classification of these subcategories in terms of the category of finite spectra. The approach presented here is purely algebraic; it is based on an analysis of pure-injective objects in a compactly generated triangulated category, and covers therefore also situations arising in algebraic geometry and representation theory.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Henning Krause
    • 1
  1. 1.Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld, Germany¶(e-mail: henning@mathematik.uni-bielefeld.de)Germany

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