Localization theories for simplicial presheaves, by P. G. Goerss and J. F. Jardine

We demonstrate that most extant localization theories for spaces, spectra and diagrams of such can be derived from a simple list of axioms which are verified in broad generality. Several new theories are introduced, including localizations for simplicial presheaves and presheaves of spectra at homology theories represented by presheaves of spectra, a theory of localization along a geometric topos morphism, and in particular a method of localizing a space or spectrum at a generalized \'etale cohomology theory. We further show that the f-localization concept has an analog for simplicial presheaves. This theory is used to answer a question of Soul\'e concerning integral homology localizations for diagrams of spaces.

This is a corrected version of this paper.

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A postscript file for this paper is available at Jardine's home page

P. G. Goerss <pgoerss@math.washington.edu>
J. F. Jardine <jardine@uwo.ca>