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...
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | INPR |
| Lenguaje: | English |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00224049_v_n_p_Cortinas |
| Aporte de: |
| id |
todo:paper_00224049_v_n_p_Cortinas |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_00224049_v_n_p_Cortinas2023-10-03T14:32:48Z Isomorphism conjectures with proper coefficients Cortiñas, G. Ellis, E. 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. INPR English info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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) |
| language |
English |
| orig_language_str_mv |
English |
| 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. |
| format |
INPR |
| author |
Cortiñas, G. Ellis, E. |
| spellingShingle |
Cortiñas, G. Ellis, E. Isomorphism conjectures with proper coefficients |
| author_facet |
Cortiñas, G. Ellis, E. |
| author_sort |
Cortiñas, G. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00224049_v_n_p_Cortinas |
| work_keys_str_mv |
AT cortinasg isomorphismconjectureswithpropercoefficients AT ellise isomorphismconjectureswithpropercoefficients |
| _version_ |
1807317968256761856 |