On some local cohomology spectral sequences

We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set.The 1st type of spectral sequences involves the left derived functors of the colimit of the direct system that we obtain by...

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Autores: Àlvarez Montaner, Josep, Fernandez Boix, Alberto, Zarzuela, Santiago
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/193547
Acceso en línea:https://hdl.handle.net/2445/193547
Access Level:acceso abierto
Palabra clave:Àlgebra homològica
Anells commutatius
Àlgebra commutativa
Successions espectrals (Matemàtica)
Topologia algebraica
Homological algebra
Commutative rings
Commutative algebra
Spectral sequences (Mathematics)
Algebraic topology
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spelling On some local cohomology spectral sequencesÀlvarez Montaner, JosepFernandez Boix, AlbertoZarzuela, SantiagoÀlgebra homològicaAnells commutatiusÀlgebra commutativaSuccessions espectrals (Matemàtica)Topologia algebraicaHomological algebraCommutative ringsCommutative algebraSpectral sequences (Mathematics)Algebraic topologyWe introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set.The 1st type of spectral sequences involves the left derived functors of the colimit of the direct system that we obtain by applying a family of functors to a single module. For the 2nd type we follow a completely different strategy as we start with the inverse system that we obtain by applying a covariant functor to an inverse system. The spectral sequences involve the right derived functors of the corresponding limit. We also have a version for contravariant functors. In all the introduced spectral sequences we provide sufficient conditions to ensure their degeneration at their 2nd page. As a consequence we obtain some decomposition theorems that greatly generalize the wellknown decomposition formula for local cohomology modules of Stanley-Reisner rings given by Hochster.Oxford University Press2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/193547Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: https://doi.org/10.1093/imrn/rny186International Mathematics Research Notices, 2018, vol. 2020, num. 19, p. 6197-6293https://doi.org/10.1093/imrn/rny186(c) Àlvarez Montaner, Josep et al., 2018info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1935472026-05-27T06:46:51Z
dc.title.none.fl_str_mv On some local cohomology spectral sequences
title On some local cohomology spectral sequences
spellingShingle On some local cohomology spectral sequences
Àlvarez Montaner, Josep
Àlgebra homològica
Anells commutatius
Àlgebra commutativa
Successions espectrals (Matemàtica)
Topologia algebraica
Homological algebra
Commutative rings
Commutative algebra
Spectral sequences (Mathematics)
Algebraic topology
title_short On some local cohomology spectral sequences
title_full On some local cohomology spectral sequences
title_fullStr On some local cohomology spectral sequences
title_full_unstemmed On some local cohomology spectral sequences
title_sort On some local cohomology spectral sequences
dc.creator.none.fl_str_mv Àlvarez Montaner, Josep
Fernandez Boix, Alberto
Zarzuela, Santiago
author Àlvarez Montaner, Josep
author_facet Àlvarez Montaner, Josep
Fernandez Boix, Alberto
Zarzuela, Santiago
author_role author
author2 Fernandez Boix, Alberto
Zarzuela, Santiago
author2_role author
author
dc.subject.none.fl_str_mv Àlgebra homològica
Anells commutatius
Àlgebra commutativa
Successions espectrals (Matemàtica)
Topologia algebraica
Homological algebra
Commutative rings
Commutative algebra
Spectral sequences (Mathematics)
Algebraic topology
topic Àlgebra homològica
Anells commutatius
Àlgebra commutativa
Successions espectrals (Matemàtica)
Topologia algebraica
Homological algebra
Commutative rings
Commutative algebra
Spectral sequences (Mathematics)
Algebraic topology
description We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set.The 1st type of spectral sequences involves the left derived functors of the colimit of the direct system that we obtain by applying a family of functors to a single module. For the 2nd type we follow a completely different strategy as we start with the inverse system that we obtain by applying a covariant functor to an inverse system. The spectral sequences involve the right derived functors of the corresponding limit. We also have a version for contravariant functors. In all the introduced spectral sequences we provide sufficient conditions to ensure their degeneration at their 2nd page. As a consequence we obtain some decomposition theorems that greatly generalize the wellknown decomposition formula for local cohomology modules of Stanley-Reisner rings given by Hochster.
publishDate 2018
dc.date.none.fl_str_mv 2018
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/2445/193547
url https://hdl.handle.net/2445/193547
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/10.1093/imrn/rny186
International Mathematics Research Notices, 2018, vol. 2020, num. 19, p. 6197-6293
https://doi.org/10.1093/imrn/rny186
dc.rights.none.fl_str_mv (c) Àlvarez Montaner, Josep et al., 2018
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Àlvarez Montaner, Josep et al., 2018
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Oxford University Press
publisher.none.fl_str_mv Oxford 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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