Algebraic & Geometric Topology

Fibre sequences and localization of simplicial sheaves

Matthias Wendt

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Abstract

In this paper, we discuss the theory of quasifibrations in proper Bousfield localizations of model categories of simplicial sheaves. We provide a construction of fibrewise localization and use this construction to generalize a criterion for locality of fibre sequences due to Berrick and Dror Farjoun. The results allow a better understanding of unstable A 1 –homotopy theory.

Article information

Source
Algebr. Geom. Topol., Volume 13, Number 3 (2013), 1779-1813.

Dates
Received: 25 April 2012
Revised: 6 February 2013
Accepted: 12 February 2013
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715600

Digital Object Identifier
doi:10.2140/agt.2013.13.1779

Mathematical Reviews number (MathSciNet)
MR3071143

Zentralblatt MATH identifier
1276.55020

Subjects
Primary: 55R65: Generalizations of fiber spaces and bundles 55P60: Localization and completion
Secondary: 18F20: Presheaves and sheaves [See also 14F05, 32C35, 32L10, 54B40, 55N30] 14F42: Motivic cohomology; motivic homotopy theory [See also 19E15]

Keywords
Bousfield localization simplicial sheaves A^1-homotopy theory

Citation

Wendt, Matthias. Fibre sequences and localization of simplicial sheaves. Algebr. Geom. Topol. 13 (2013), no. 3, 1779--1813. doi:10.2140/agt.2013.13.1779. https://projecteuclid.org/euclid.agt/1513715600


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References

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