The obstruction to excision in K-theory and in cyclic homology

Let f: A → B be a ring homomorphism of not necessarily unital rings and I A an ideal which is mapped by f isomorphically to an ideal of B. The obstruction to excision in K-theory is the failure of the map between relative K-groups K *(A:I)→K *(B:f(I)) to be an isomorphism; it is measured by the bire...

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Detalhes bibliográficos
Autor: Cortiñas, Guillermo Horacio
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2006
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositório:CONICET Digital (CONICET)
Idioma:inglês
OAI Identifier:oai:ri.conicet.gov.ar:11336/151169
Acesso em linha:http://hdl.handle.net/11336/151169
Access Level:Acceso aberto
Palavra-chave:RING HOMOMORPHISM
UNITAL RING
CHERN CHARACTER
CYCLIC HOMOLOGY
NEGATIVE CYCLIC HOMOLOGY
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling The obstruction to excision in K-theory and in cyclic homologyCortiñas, Guillermo HoracioRING HOMOMORPHISMUNITAL RINGCHERN CHARACTERCYCLIC HOMOLOGYNEGATIVE CYCLIC HOMOLOGYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let f: A → B be a ring homomorphism of not necessarily unital rings and I A an ideal which is mapped by f isomorphically to an ideal of B. The obstruction to excision in K-theory is the failure of the map between relative K-groups K *(A:I)→K *(B:f(I)) to be an isomorphism; it is measured by the birelative groups K *(A,B:I) . Similarly the groups HN *(A,B:I) measure the obstruction to excision in negative cyclic homology. We show that the rational Jones-Goodwillie Chern character induces an isomorphism ch *:K *(A,B:I)⊗ ℚ →simHN * A ⊗ℚ,B ⊗ℚ:I ⊗ℚ.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"; ArgentinaSpringer2006-12info: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/11336/151169Cortiñas, Guillermo Horacio; The obstruction to excision in K-theory and in cyclic homology; Springer; Inventiones Mathematicae; 164; 1; 12-2006; 143-1730020-9910CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00222-005-0473-9info:eu-repo/semantics/altIdentifier/doi/10.1007/s00222-005-0473-9info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/math/0111096info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T14:27:32Zoai:ri.conicet.gov.ar:11336/151169instacron: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:34982024-05-08 14:27:32.396CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The obstruction to excision in K-theory and in cyclic homology
title The obstruction to excision in K-theory and in cyclic homology
spellingShingle The obstruction to excision in K-theory and in cyclic homology
Cortiñas, Guillermo Horacio
RING HOMOMORPHISM
UNITAL RING
CHERN CHARACTER
CYCLIC HOMOLOGY
NEGATIVE CYCLIC HOMOLOGY
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short The obstruction to excision in K-theory and in cyclic homology
title_full The obstruction to excision in K-theory and in cyclic homology
title_fullStr The obstruction to excision in K-theory and in cyclic homology
title_full_unstemmed The obstruction to excision in K-theory and in cyclic homology
title_sort The obstruction to excision in K-theory and in cyclic homology
dc.creator.none.fl_str_mv Cortiñas, Guillermo Horacio
author Cortiñas, Guillermo Horacio
author_facet Cortiñas, Guillermo Horacio
author_role author
dc.subject.none.fl_str_mv RING HOMOMORPHISM
UNITAL RING
CHERN CHARACTER
CYCLIC HOMOLOGY
NEGATIVE CYCLIC HOMOLOGY
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic RING HOMOMORPHISM
UNITAL RING
CHERN CHARACTER
CYCLIC HOMOLOGY
NEGATIVE CYCLIC HOMOLOGY
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description Let f: A → B be a ring homomorphism of not necessarily unital rings and I A an ideal which is mapped by f isomorphically to an ideal of B. The obstruction to excision in K-theory is the failure of the map between relative K-groups K *(A:I)→K *(B:f(I)) to be an isomorphism; it is measured by the birelative groups K *(A,B:I) . Similarly the groups HN *(A,B:I) measure the obstruction to excision in negative cyclic homology. We show that the rational Jones-Goodwillie Chern character induces an isomorphism ch *:K *(A,B:I)⊗ ℚ →simHN * A ⊗ℚ,B ⊗ℚ:I ⊗ℚ.
publishDate 2006
dc.date.none.fl_str_mv 2006-12
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/11336/151169
Cortiñas, Guillermo Horacio; The obstruction to excision in K-theory and in cyclic homology; Springer; Inventiones Mathematicae; 164; 1; 12-2006; 143-173
0020-9910
CONICET Digital
CONICET
url http://hdl.handle.net/11336/151169
identifier_str_mv Cortiñas, Guillermo Horacio; The obstruction to excision in K-theory and in cyclic homology; Springer; Inventiones Mathematicae; 164; 1; 12-2006; 143-173
0020-9910
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00222-005-0473-9
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00222-005-0473-9
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/math/0111096
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 Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15,811543

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