On determinant functors and K-theory

We extend Deligne’s notion of determinant functor to Waldhausen categories and (strongly) triangulated categories. We construct explicit universal determinant functors in each case, whose target is an algebraic model for the 1-type of the corresponding K-theory spectrum. As applications, we answer o...

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Detalles Bibliográficos
Autores: Muro Jiménez, Fernando, Tonks, Andrew, Witte, Malte
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41875
Acceso en línea:http://hdl.handle.net/11441/41875
https://doi.org/10.5565/PUBLMAT_59115_07
Access Level:acceso abierto
Palabra clave:Determinant functor
K-theory
exact category
Waldhausen category
triangulated category
Grothendieck derivator
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spelling On determinant functors and K-theoryMuro Jiménez, FernandoTonks, AndrewWitte, MalteDeterminant functorK-theoryexact categoryWaldhausen categorytriangulated categoryGrothendieck derivatorWe extend Deligne’s notion of determinant functor to Waldhausen categories and (strongly) triangulated categories. We construct explicit universal determinant functors in each case, whose target is an algebraic model for the 1-type of the corresponding K-theory spectrum. As applications, we answer open questions by Maltsiniotis and Neeman on the K-theory of (strongly) triangulated categories and a question of Grothendieck to Knudsen on determinant functors. We also prove additivity theorems for low-dimensional K-theory of (strongly) triangulated categories and obtain generators and (some) relations for various K1-groups. This is achieved via a unified theory of determinant functors which can be applied in further contexts, such as derivators.Ministerio de Economía y CompetitividadGeneralitat de CatalunyaJunta de Andalucía. Consejería de Economía, Innovación y CienciaUniversitat Autònoma de BarcelonaÁlgebra2015info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/41875https://doi.org/10.5565/PUBLMAT_59115_07reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésPublicacions matemàtiques, 59 (1), 137-233.info:eu-repo/grantAgreement/MINECO/MTM2010-15831/info:eu-repo/grantAgreement/MINECO/MTM2013- 42178-P/SGR-119-2009FQM-5713http://dx.doi.org/10.5565/PUBLMAT_59115_07info:eu-repo/semantics/openAccessoai:idus.us.es:11441/418752026-06-17T12:51:07Z
dc.title.none.fl_str_mv On determinant functors and K-theory
title On determinant functors and K-theory
spellingShingle On determinant functors and K-theory
Muro Jiménez, Fernando
Determinant functor
K-theory
exact category
Waldhausen category
triangulated category
Grothendieck derivator
title_short On determinant functors and K-theory
title_full On determinant functors and K-theory
title_fullStr On determinant functors and K-theory
title_full_unstemmed On determinant functors and K-theory
title_sort On determinant functors and K-theory
dc.creator.none.fl_str_mv Muro Jiménez, Fernando
Tonks, Andrew
Witte, Malte
author Muro Jiménez, Fernando
author_facet Muro Jiménez, Fernando
Tonks, Andrew
Witte, Malte
author_role author
author2 Tonks, Andrew
Witte, Malte
author2_role author
author
dc.contributor.none.fl_str_mv Álgebra
dc.subject.none.fl_str_mv Determinant functor
K-theory
exact category
Waldhausen category
triangulated category
Grothendieck derivator
topic Determinant functor
K-theory
exact category
Waldhausen category
triangulated category
Grothendieck derivator
description We extend Deligne’s notion of determinant functor to Waldhausen categories and (strongly) triangulated categories. We construct explicit universal determinant functors in each case, whose target is an algebraic model for the 1-type of the corresponding K-theory spectrum. As applications, we answer open questions by Maltsiniotis and Neeman on the K-theory of (strongly) triangulated categories and a question of Grothendieck to Knudsen on determinant functors. We also prove additivity theorems for low-dimensional K-theory of (strongly) triangulated categories and obtain generators and (some) relations for various K1-groups. This is achieved via a unified theory of determinant functors which can be applied in further contexts, such as derivators.
publishDate 2015
dc.date.none.fl_str_mv 2015
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/41875
https://doi.org/10.5565/PUBLMAT_59115_07
url http://hdl.handle.net/11441/41875
https://doi.org/10.5565/PUBLMAT_59115_07
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Publicacions matemàtiques, 59 (1), 137-233.
info:eu-repo/grantAgreement/MINECO/MTM2010-15831/
info:eu-repo/grantAgreement/MINECO/MTM2013- 42178-P/
SGR-119-2009
FQM-5713
http://dx.doi.org/10.5565/PUBLMAT_59115_07
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Universitat Autònoma de Barcelona
publisher.none.fl_str_mv Universitat Autònoma de Barcelona
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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