Algebraic & Geometric Topology

Fibre sequences and localization of simplicial sheaves

Matthias Wendt

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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

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

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

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Zentralblatt MATH identifier

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]

Bousfield localization simplicial sheaves A^1-homotopy theory


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.

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