Abstract

We construct an abelian category A(G) of sheaves over a category of closed subgroups of the r-torus G. The category A(G) is of injective dimension r, and can be used as a model for rational G-spectra. Indeed, we show that there is a homology theory A : G-spectra ! A(G) on rational G-spectra with values in A(G) and the associated Adams spectral sequence converges for all rational G-spectra and collapses at a nite stage. This is the rst paper in a series of three. It culminates in [8] where the author and B.E.Shipley combine the Adams spectral sequence constructed here with the enriched Morita equivalence of Schwede and Shipley [9] to deduce that the category of dierential graded objects of A(G) is Quillen equivalent to the category of rational G-spectra. Contents Part 1.

Citations