FoCM

Conference abstracts


Session S10 - Homological Methods

July 29, 16:30 ~ 17:00

Isomorphism conjectures with proper coefficients

Eugenia Ellis

Universidad de la República, Uruguay   -   eellis@fing.edu.uy

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 HG(G/H,E(A))=E(AH). The strong isomorphism conjecture for the quadruple (G,F,E,A) asserts that if XY is an equivariant map such that XHYH is an equivalence for all HF, then HG(X,E(A))HG(Y,E(A)) is an equivalence. We introduce an algebraic notion of (G,F)-properness for G-rings, modelled 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.

Joint work with Guillermo Cortiñas (Universidad de Buenos Aires, Argentina).

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