## Smashing Subcategories And The Telescope Conjecture - An Algebraic Approach (1998)

Venue: | Invent. Math |

Citations: | 25 - 6 self |

### BibTeX

@ARTICLE{Krause98smashingsubcategories,

author = {Henning Krause},

title = {Smashing Subcategories And The Telescope Conjecture - An Algebraic Approach},

journal = {Invent. Math},

year = {1998},

volume = {139},

pages = {99--133}

}

### OpenURL

### 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. Introduction Smashing subcategories naturally arise in the stable homotopy category S from localization functors l : S ! S which induce for every spectrum X a natural isomorphism l(X) ' X l(S) between the localization of X and the smash product of X with the localization of the sphere spectrum S. In fact, a localization functor has this property if and only if it preserv...