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(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, 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).