Inventiones mathematicae

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

Smashing subcategories and the telescope conjecture – an algebraic approach

  • Henning Krause


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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:

Personalised recommendations