A Quillen model structure of local homotopy equivalences

Autores
Mukherjee, Devarshi; Cortiñas, Guillermo Horacio
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this note, we construct a closed model structure on the category of Z/2Z-graded complexes of projective systems of ind-Banach spaces. When the base field is the fraction field F of a complete discrete valuation ring V, the homotopy category of this model category is the derived category of Z/2Z -graded complexes of the quasi-abelian category Ind(Ban_F). This homotopy category is the appropriate target of the local and analytic cyclic homology theories for complete, torsionfree V-algebras and F-algebras. When the base field is C, the homotopy category is the target of local and analytic cyclic homology for pro-bornological C-algebras, which includes the subcategory of pro-C*-algebras.
Fil: Mukherjee, Devarshi. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Cortiñas, Guillermo Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
MODEL CATEGORIES
CYCLIC HOMOLOGY
FUNCTIONAL ANALYSIS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/243999
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A Quillen model structure of local homotopy equivalencesMukherjee, DevarshiCortiñas, Guillermo HoracioMODEL CATEGORIESCYCLIC HOMOLOGYFUNCTIONAL ANALYSIShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this note, we construct a closed model structure on the category of Z/2Z-graded complexes of projective systems of ind-Banach spaces. When the base field is the fraction field F of a complete discrete valuation ring V, the homotopy category of this model category is the derived category of Z/2Z -graded complexes of the quasi-abelian category Ind(Ban_F). This homotopy category is the appropriate target of the local and analytic cyclic homology theories for complete, torsionfree V-algebras and F-algebras. When the base field is C, the homotopy category is the target of local and analytic cyclic homology for pro-bornological C-algebras, which includes the subcategory of pro-C*-algebras.Fil: Mukherjee, Devarshi. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Cortiñas, Guillermo Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaMount Allison University2024-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/243999Mukherjee, Devarshi; Cortiñas, Guillermo Horacio; A Quillen model structure of local homotopy equivalences; Mount Allison University; Theory And Applications Of Categories; 41; 9; 3-2024; 268-2871201-561XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.tac.mta.ca/tac/volumes/41/9/41-09abs.htmlinfo:eu-repo/semantics/altIdentifier/url/http://www.tac.mta.ca/tac/volumes/41/9/41-09.pdfinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2207.02979info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2207.02979info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:35:23Zoai:ri.conicet.gov.ar:11336/243999instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-12 09:35:23.272CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A Quillen model structure of local homotopy equivalences
title A Quillen model structure of local homotopy equivalences
spellingShingle A Quillen model structure of local homotopy equivalences
Mukherjee, Devarshi
MODEL CATEGORIES
CYCLIC HOMOLOGY
FUNCTIONAL ANALYSIS
title_short A Quillen model structure of local homotopy equivalences
title_full A Quillen model structure of local homotopy equivalences
title_fullStr A Quillen model structure of local homotopy equivalences
title_full_unstemmed A Quillen model structure of local homotopy equivalences
title_sort A Quillen model structure of local homotopy equivalences
dc.creator.none.fl_str_mv Mukherjee, Devarshi
Cortiñas, Guillermo Horacio
author Mukherjee, Devarshi
author_facet Mukherjee, Devarshi
Cortiñas, Guillermo Horacio
author_role author
author2 Cortiñas, Guillermo Horacio
author2_role author
dc.subject.none.fl_str_mv MODEL CATEGORIES
CYCLIC HOMOLOGY
FUNCTIONAL ANALYSIS
topic MODEL CATEGORIES
CYCLIC HOMOLOGY
FUNCTIONAL ANALYSIS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this note, we construct a closed model structure on the category of Z/2Z-graded complexes of projective systems of ind-Banach spaces. When the base field is the fraction field F of a complete discrete valuation ring V, the homotopy category of this model category is the derived category of Z/2Z -graded complexes of the quasi-abelian category Ind(Ban_F). This homotopy category is the appropriate target of the local and analytic cyclic homology theories for complete, torsionfree V-algebras and F-algebras. When the base field is C, the homotopy category is the target of local and analytic cyclic homology for pro-bornological C-algebras, which includes the subcategory of pro-C*-algebras.
Fil: Mukherjee, Devarshi. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Cortiñas, Guillermo Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description In this note, we construct a closed model structure on the category of Z/2Z-graded complexes of projective systems of ind-Banach spaces. When the base field is the fraction field F of a complete discrete valuation ring V, the homotopy category of this model category is the derived category of Z/2Z -graded complexes of the quasi-abelian category Ind(Ban_F). This homotopy category is the appropriate target of the local and analytic cyclic homology theories for complete, torsionfree V-algebras and F-algebras. When the base field is C, the homotopy category is the target of local and analytic cyclic homology for pro-bornological C-algebras, which includes the subcategory of pro-C*-algebras.
publishDate 2024
dc.date.none.fl_str_mv 2024-03
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/243999
Mukherjee, Devarshi; Cortiñas, Guillermo Horacio; A Quillen model structure of local homotopy equivalences; Mount Allison University; Theory And Applications Of Categories; 41; 9; 3-2024; 268-287
1201-561X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/243999
identifier_str_mv Mukherjee, Devarshi; Cortiñas, Guillermo Horacio; A Quillen model structure of local homotopy equivalences; Mount Allison University; Theory And Applications Of Categories; 41; 9; 3-2024; 268-287
1201-561X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.tac.mta.ca/tac/volumes/41/9/41-09abs.html
info:eu-repo/semantics/altIdentifier/url/http://www.tac.mta.ca/tac/volumes/41/9/41-09.pdf
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2207.02979
info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2207.02979
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Mount Allison University
publisher.none.fl_str_mv Mount Allison University
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.976206

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