Fibre sequences and localization of simplicial sheaves

Wendt, Matthias

doi:10.2140/agt.2013.13.1779

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Fibre sequences and localization of simplicial sheaves

Matthias Wendt

Algebraic & Geometric Topology 13 (2013) 1779–1813

DOI: 10.2140/agt.2013.13.1779

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 $A^{1}$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mrow><mi mathvariant="double-struck">A</mi></mrow><mrow><mn>1</mn></mrow></msup></math>$ –homotopy theory.

Keywords

Bousfield localization, simplicial sheaves, A^1-homotopy theory

Mathematical Subject Classification 2010

Primary: 55R65, 55P60

Secondary: 18F20, 14F42

References

Publication

Received: 25 April 2012

Revised: 6 February 2013

Accepted: 12 February 2013

Published: 19 May 2013

Authors

Matthias Wendt
Mathematisches Institut Albert-Ludwigs-Universität Freiburg Eckerstraße 1 D-79104, Freiburg im Breisgau Germany

Volume 13, issue 3 (2013)