Model category structures and spectral sequences

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 associa...

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Authors: Cirici, Joana, Egas Santander, Daniela, Livernet, Muriel, Whitehouse, Sarah
Format: article
Status:Versión aceptada para publicación
Publication Date:2019
Country:España
Institution:Universidad de Barcelona
Repository:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/192306
Online Access:https://hdl.handle.net/2445/192306
Access Level:Open access
Keyword:Àlgebra homològica
Teoria de l'homotopia
Topologia algebraica
Homological algebra
Homotopy theory
Algebraic topology
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spelling Model category structures and spectral sequencesCirici, JoanaEgas Santander, DanielaLivernet, MurielWhitehouse, SarahÀlgebra homològicaTeoria de l'homotopiaTopologia algebraicaHomological algebraHomotopy theoryAlgebraic topologyLet $R$ 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.Cambridge University Press2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/192306Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: https://doi.org/10.1017/prm.2019.45Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2019, vol. 150, num. 6, p. 2815-2848https://doi.org/10.1017/prm.2019.45(c) Royal Society of Edinburgh , 2019info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1923062026-05-27T06:46:51Z
dc.title.none.fl_str_mv Model category structures and spectral sequences
title Model category structures and spectral sequences
spellingShingle Model category structures and spectral sequences
Cirici, Joana
Àlgebra homològica
Teoria de l'homotopia
Topologia algebraica
Homological algebra
Homotopy theory
Algebraic topology
title_short Model category structures and spectral sequences
title_full Model category structures and spectral sequences
title_fullStr Model category structures and spectral sequences
title_full_unstemmed Model category structures and spectral sequences
title_sort Model category structures and spectral sequences
dc.creator.none.fl_str_mv Cirici, Joana
Egas Santander, Daniela
Livernet, Muriel
Whitehouse, Sarah
author Cirici, Joana
author_facet Cirici, Joana
Egas Santander, Daniela
Livernet, Muriel
Whitehouse, Sarah
author_role author
author2 Egas Santander, Daniela
Livernet, Muriel
Whitehouse, Sarah
author2_role author
author
author
dc.subject.none.fl_str_mv Àlgebra homològica
Teoria de l'homotopia
Topologia algebraica
Homological algebra
Homotopy theory
Algebraic topology
topic Àlgebra homològica
Teoria de l'homotopia
Topologia algebraica
Homological algebra
Homotopy theory
Algebraic topology
description 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.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/192306
url https://hdl.handle.net/2445/192306
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1017/prm.2019.45
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2019, vol. 150, num. 6, p. 2815-2848
https://doi.org/10.1017/prm.2019.45
dc.rights.none.fl_str_mv (c) Royal Society of Edinburgh , 2019
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Royal Society of Edinburgh , 2019
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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