### 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>