Isomorphism conjectures with proper coefficients
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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paper:paper_00224049_v218_n7_p1224_Cortinas2023-06-08T14:50:43Z 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. Fil:Cortiñas, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v218_n7_p1224_Cortinas http://hdl.handle.net/20.500.12110/paper_00224049_v218_n7_p1224_Cortinas |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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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. |
| 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 |
2014 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v218_n7_p1224_Cortinas http://hdl.handle.net/20.500.12110/paper_00224049_v218_n7_p1224_Cortinas |
| work_keys_str_mv |
AT cortinasguillermohoracio isomorphismconjectureswithpropercoefficients |
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1768546008236556288 |