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.
Documento: | Artículo |
Título: | Isomorphism conjectures with proper coefficients |
Autor: | Cortiñas, G.; Ellis, E. |
Filiación: | Dep. Matemática-IMAS, FCEyN-UBA, Ciudad Universitaria Pab 1, 1428 Buenos Aires, Argentina Centro de Matemática, Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400 Montevideo, Uruguay |
Idioma: | Inglés |
Año: | 2013 |
DOI: | http://dx.doi.org/10.1016/j.jpaa.2013.11.016 |
Título revista: | Journal of Pure and Applied Algebra |
Título revista abreviado: | J. Pure Appl. Algebra |
ISSN: | 00224049 |
CODEN: | JPAAA |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v_n_p_Cortinas |