Localization theories for simplicial presheaves

P. G. Goerss; J. F. Jardine

doi:10.4153/CJM-1998-051-1

Localization theories for simplicial presheaves

P. G. Goerss^*, J. F. Jardine

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

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 double-struck A¹-local theory of Morel-Voevodsky. This theory answers a question of Soulé concerning integral homology localizations for diagrams of spaces.

Original language	English (US)
Pages (from-to)	1048-1089
Number of pages	42
Journal	Canadian Journal of Mathematics
Volume	50
Issue number	5
DOIs	https://doi.org/10.4153/CJM-1998-051-1
State	Published - Oct 1998

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General Mathematics

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AB - 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 double-struck A1-local theory of Morel-Voevodsky. This theory answers a question of Soulé concerning integral homology localizations for diagrams of spaces.

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Localization theories for simplicial presheaves

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