Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces

ABSTRACT. We describe the $E$-infinity algebra structure on the complex of singular cochains of a topological space, in the context of sheaf theory. As a first application, for any algebraic variety we define a weight filtration compatible with its $E$-infinity structure. This naturally extends the...

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Detalles Bibliográficos
Autores: Chataur, David, Cirici, Joana
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2022
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/190227
Acceso en línea:https://hdl.handle.net/2445/190227
Access Level:acceso abierto
Palabra clave:Topologia algebraica
Homologia
Teoria de Hodge
Algebraic topology
Homology
Hodge theory
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spelling Sheaves of E-infinity algebras and applications to algebraic varieties and singular spacesChataur, DavidCirici, JoanaTopologia algebraicaHomologiaTeoria de HodgeAlgebraic topologyHomologyHodge theoryABSTRACT. We describe the $E$-infinity algebra structure on the complex of singular cochains of a topological space, in the context of sheaf theory. As a first application, for any algebraic variety we define a weight filtration compatible with its $E$-infinity structure. This naturally extends the theory of mixed Hodge structures in rational homotopy to $p$-adic homotopy theory. The spectral sequence associated to the weight filtration gives a new family of algebraic invariants of the varieties for any coefficient ring, carrying Steenrod operations. As a second application, we promote Deligne's intersection complex computing intersection cohomology, to a sheaf carrying E-infinity structures. This allows for a natural interpretation of the Steenrod operations defined on the intersection cohomology of any topological pseudomanifold.American Mathematical Society (AMS)2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/190227Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: https://doi.org/10.1090/tran/8569Transactions of the American Mathematical Society, 2022, vol. 375, num. 2, p. 925-960https://doi.org/10.1090/tran/8569cc-by-nc-nd (c) American Mathematical Society (AMS), 2022https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1902272026-05-27T06:46:51Z
dc.title.none.fl_str_mv Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces
title Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces
spellingShingle Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces
Chataur, David
Topologia algebraica
Homologia
Teoria de Hodge
Algebraic topology
Homology
Hodge theory
title_short Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces
title_full Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces
title_fullStr Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces
title_full_unstemmed Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces
title_sort Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces
dc.creator.none.fl_str_mv Chataur, David
Cirici, Joana
author Chataur, David
author_facet Chataur, David
Cirici, Joana
author_role author
author2 Cirici, Joana
author2_role author
dc.subject.none.fl_str_mv Topologia algebraica
Homologia
Teoria de Hodge
Algebraic topology
Homology
Hodge theory
topic Topologia algebraica
Homologia
Teoria de Hodge
Algebraic topology
Homology
Hodge theory
description ABSTRACT. We describe the $E$-infinity algebra structure on the complex of singular cochains of a topological space, in the context of sheaf theory. As a first application, for any algebraic variety we define a weight filtration compatible with its $E$-infinity structure. This naturally extends the theory of mixed Hodge structures in rational homotopy to $p$-adic homotopy theory. The spectral sequence associated to the weight filtration gives a new family of algebraic invariants of the varieties for any coefficient ring, carrying Steenrod operations. As a second application, we promote Deligne's intersection complex computing intersection cohomology, to a sheaf carrying E-infinity structures. This allows for a natural interpretation of the Steenrod operations defined on the intersection cohomology of any topological pseudomanifold.
publishDate 2022
dc.date.none.fl_str_mv 2022
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/2445/190227
url https://hdl.handle.net/2445/190227
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/10.1090/tran/8569
Transactions of the American Mathematical Society, 2022, vol. 375, num. 2, p. 925-960
https://doi.org/10.1090/tran/8569
dc.rights.none.fl_str_mv cc-by-nc-nd (c) American Mathematical Society (AMS), 2022
https://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) American Mathematical Society (AMS), 2022
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society (AMS)
publisher.none.fl_str_mv American Mathematical Society (AMS)
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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