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# Localization theories for simplicial presheaves

Published:1998-10-01
Printed: Oct 1998
• P. G. Goerss
• J. F. Jardine
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## Abstract

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, and a theory of localization along a geometric topos morphism. The $f$-localization concept has an analog for simplicial presheaves, and specializes to the $\hbox{\Bbbvii A}^1$-local theory of Morel-Voevodsky. This theory answers a question of Soul\'e concerning integral homology localizations for diagrams of spaces.
 MSC Classifications: 55P60 - Localization and completion 19E08 - $K$-theory of schemes [See also 14C35] 18F20 - Presheaves and sheaves [See also 14F05, 32C35, 32L10, 54B40, 55N30]

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