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Abstract:

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.

Registro:

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
Año:2014
Volumen:218
Número:7
Página de inicio:1224
Página de fin:1263
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_v218_n7_p1224_Cortinas

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Citas:

---------- APA ----------
Cortiñas, G. & Ellis, E. (2014) . Isomorphism conjectures with proper coefficients. Journal of Pure and Applied Algebra, 218(7), 1224-1263.
http://dx.doi.org/10.1016/j.jpaa.2013.11.016
---------- CHICAGO ----------
Cortiñas, G., Ellis, E. "Isomorphism conjectures with proper coefficients" . Journal of Pure and Applied Algebra 218, no. 7 (2014) : 1224-1263.
http://dx.doi.org/10.1016/j.jpaa.2013.11.016
---------- MLA ----------
Cortiñas, G., Ellis, E. "Isomorphism conjectures with proper coefficients" . Journal of Pure and Applied Algebra, vol. 218, no. 7, 2014, pp. 1224-1263.
http://dx.doi.org/10.1016/j.jpaa.2013.11.016
---------- VANCOUVER ----------
Cortiñas, G., Ellis, E. Isomorphism conjectures with proper coefficients. J. Pure Appl. Algebra. 2014;218(7):1224-1263.
http://dx.doi.org/10.1016/j.jpaa.2013.11.016