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Model category structures and spectral sequences

Part of: Homological algebra

Published online by Cambridge University Press:  01 August 2019

Joana Cirici ,
Daniela Egas Santander ,
Muriel Livernet  and
Sarah Whitehouse
Joana Cirici
Affiliation:
Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via 585 08007 Barcelona, Spain (jcirici@ub.edu)
Daniela Egas Santander
Affiliation:
Ecole polytechnique fédérale de Lausanne, SV BMI UPHESS, MA B3 425 (Bâtiment MA), Station 8, CH-1015 Lausanne, Switzerland (daniela.egassantander@epfl.ch)
Muriel Livernet
Affiliation:
Univ Paris Diderot, Institut de Mathématiques de Jussieu-Paris Rive Gauche, CNRS, Sorbonne Université, 8 place Aurélie Nemours, F-75013, Paris, France (livernet@math.univ-paris-diderot.fr)
Sarah Whitehouse
Affiliation:
School of Mathematics and Statistics, University of Sheffield S3 7RH, Sheffield, England (s.whitehouse@sheffield.ac.uk)
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Abstract

Let R be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of R-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a quasi-isomorphism at a certain fixed stage of the associated spectral sequence. For filtered complexes, we relate the different model structures obtained, when we vary the stage of the spectral sequence, using the functors shift and décalage.

Keywords

filtered complexbicomplexspectral sequencemodel category

MSC classification

Primary: 18G55: Homotopical algebra
Secondary: 18G40: Spectral sequences, hypercohomology
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 6 , December 2020 , pp. 2815 - 2848
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Copyright
Copyright © 2019 The Royal Society of Edinburgh

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