Isomorphism conjectures with proper coefficients

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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...

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Autor principal: Cortiñas, Guillermo Horacio
Publicado: 2013
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v_n_p_Cortinas
http://hdl.handle.net/20.500.12110/paper_00224049_v_n_p_Cortinas
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_00224049_v_n_p_Cortinas2023-06-08T14:50:47Z Isomorphism conjectures with proper coefficients Cortiñas, Guillermo Horacio 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, thenHG (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. © 2013 Elsevier B.V. All rights reserved. Fil:Cortiñas, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2013 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v_n_p_Cortinas http://hdl.handle.net/20.500.12110/paper_00224049_v_n_p_Cortinas
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
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, thenHG (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. © 2013 Elsevier B.V. All rights reserved.
author Cortiñas, Guillermo Horacio
spellingShingle Cortiñas, Guillermo Horacio
Isomorphism conjectures with proper coefficients
author_facet Cortiñas, Guillermo Horacio
author_sort Cortiñas, Guillermo Horacio
title Isomorphism conjectures with proper coefficients
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
publishDate 2013
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v_n_p_Cortinas
http://hdl.handle.net/20.500.12110/paper_00224049_v_n_p_Cortinas
work_keys_str_mv AT cortinasguillermohoracio isomorphismconjectureswithpropercoefficients
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