Isomorphism conjectures with proper coefficients
- Autores
- Cortiñas, Guillermo Horacio; Ellis, Eugenia
- Año de publicación
- 2014
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Let G be a group and F a nonempty family of subgroups of G, closed under conjugation and under subgroups. Also let E be a functor from small Z-linear categories to spectra, and let A be a ring with a G-action. Under mild conditions on E and A one can define an equivariant homology theory HG(−,E(A)) of G-simplicial sets such that H⁎G(G/H,E(A))=E(A⋊H). The strong isomorphism conjecture for the quadruple (G,F,E,A) asserts that if X→Y is an equivariant map such that XH→YH is an equivalence for all H∈F, then HG(X,E(A))→HG(Y,E(A)) is an equivalence. In this paper we introduce an algebraic notion of (G,F)-properness for G-rings, modeled on the analogous notion for G-C-algebras, and show that the strong (G,F,E,P) isomorphism conjecture for (G,F)-proper P is true in several cases of interest in the algebraic K-theory context.
Fil: Cortiñas, Guillermo Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
Fil: Ellis, Eugenia. Universidad de la República; Uruguay - Materia
- Farrell-Jones Conjecture
- Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/18780
Ver los metadatos del registro completo
| id |
CONICETDig_b2264f8017867b34cc543271b702de50 |
|---|---|
| oai_identifier_str |
oai:ri.conicet.gov.ar:11336/18780 |
| network_acronym_str |
CONICETDig |
| repository_id_str |
3498 |
| network_name_str |
CONICET Digital (CONICET) |
| spelling |
Isomorphism conjectures with proper coefficientsCortiñas, Guillermo HoracioEllis, EugeniaFarrell-Jones Conjecturehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let G be a group and F a nonempty family of subgroups of G, closed under conjugation and under subgroups. Also let E be a functor from small Z-linear categories to spectra, and let A be a ring with a G-action. Under mild conditions on E and A one can define an equivariant homology theory HG(−,E(A)) of G-simplicial sets such that H⁎G(G/H,E(A))=E(A⋊H). The strong isomorphism conjecture for the quadruple (G,F,E,A) asserts that if X→Y is an equivariant map such that XH→YH is an equivalence for all H∈F, then HG(X,E(A))→HG(Y,E(A)) is an equivalence. In this paper we introduce an algebraic notion of (G,F)-properness for G-rings, modeled on the analogous notion for G-C-algebras, and show that the strong (G,F,E,P) isomorphism conjecture for (G,F)-proper P is true in several cases of interest in the algebraic K-theory context.Fil: Cortiñas, Guillermo Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaFil: Ellis, Eugenia. Universidad de la República; UruguayElsevier Science2014-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18780Cortiñas, Guillermo Horacio; Ellis, Eugenia; Isomorphism conjectures with proper coefficients; Elsevier Science; Journal Of Pure And Applied Algebra; 218; 7; 7-2014; 1224-12630022-4049CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2013.11.016info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S002240491300220Xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:03:34Zoai:ri.conicet.gov.ar:11336/18780instacron: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:34982025-09-03 10:03:35.173CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
Isomorphism conjectures with proper coefficients |
| title |
Isomorphism conjectures with proper coefficients |
| spellingShingle |
Isomorphism conjectures with proper coefficients Cortiñas, Guillermo Horacio Farrell-Jones Conjecture |
| title_short |
Isomorphism conjectures with proper coefficients |
| title_full |
Isomorphism conjectures with proper coefficients |
| title_fullStr |
Isomorphism conjectures with proper coefficients |
| title_full_unstemmed |
Isomorphism conjectures with proper coefficients |
| title_sort |
Isomorphism conjectures with proper coefficients |
| dc.creator.none.fl_str_mv |
Cortiñas, Guillermo Horacio Ellis, Eugenia |
| author |
Cortiñas, Guillermo Horacio |
| author_facet |
Cortiñas, Guillermo Horacio Ellis, Eugenia |
| author_role |
author |
| author2 |
Ellis, Eugenia |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Farrell-Jones Conjecture |
| topic |
Farrell-Jones Conjecture |
| purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| dc.description.none.fl_txt_mv |
Let G be a group and F a nonempty family of subgroups of G, closed under conjugation and under subgroups. Also let E be a functor from small Z-linear categories to spectra, and let A be a ring with a G-action. Under mild conditions on E and A one can define an equivariant homology theory HG(−,E(A)) of G-simplicial sets such that H⁎G(G/H,E(A))=E(A⋊H). The strong isomorphism conjecture for the quadruple (G,F,E,A) asserts that if X→Y is an equivariant map such that XH→YH is an equivalence for all H∈F, then HG(X,E(A))→HG(Y,E(A)) is an equivalence. In this paper we introduce an algebraic notion of (G,F)-properness for G-rings, modeled on the analogous notion for G-C-algebras, and show that the strong (G,F,E,P) isomorphism conjecture for (G,F)-proper P is true in several cases of interest in the algebraic K-theory context. Fil: Cortiñas, Guillermo Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina Fil: Ellis, Eugenia. Universidad de la República; Uruguay |
| description |
Let G be a group and F a nonempty family of subgroups of G, closed under conjugation and under subgroups. Also let E be a functor from small Z-linear categories to spectra, and let A be a ring with a G-action. Under mild conditions on E and A one can define an equivariant homology theory HG(−,E(A)) of G-simplicial sets such that H⁎G(G/H,E(A))=E(A⋊H). The strong isomorphism conjecture for the quadruple (G,F,E,A) asserts that if X→Y is an equivariant map such that XH→YH is an equivalence for all H∈F, then HG(X,E(A))→HG(Y,E(A)) is an equivalence. In this paper we introduce an algebraic notion of (G,F)-properness for G-rings, modeled on the analogous notion for G-C-algebras, and show that the strong (G,F,E,P) isomorphism conjecture for (G,F)-proper P is true in several cases of interest in the algebraic K-theory context. |
| publishDate |
2014 |
| dc.date.none.fl_str_mv |
2014-07 |
| 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/11336/18780 Cortiñas, Guillermo Horacio; Ellis, Eugenia; Isomorphism conjectures with proper coefficients; Elsevier Science; Journal Of Pure And Applied Algebra; 218; 7; 7-2014; 1224-1263 0022-4049 CONICET Digital CONICET |
| url |
http://hdl.handle.net/11336/18780 |
| identifier_str_mv |
Cortiñas, Guillermo Horacio; Ellis, Eugenia; Isomorphism conjectures with proper coefficients; Elsevier Science; Journal Of Pure And Applied Algebra; 218; 7; 7-2014; 1224-1263 0022-4049 CONICET Digital CONICET |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2013.11.016 info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S002240491300220X |
| 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 |
| dc.publisher.none.fl_str_mv |
Elsevier Science |
| publisher.none.fl_str_mv |
Elsevier Science |
| 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 |
| _version_ |
1842269808284925952 |
| score |
13.13397 |