Rational torus-equivariant stable homotopy V: the torsion Adams spectral sequence

Abstract: We provide a calculational method for rational stable equivariant homotopy theory for a torus G based on the homology of the Borel construction on fixed points. More precisely we define an abelian torsion model, A_t(G) of finite injective dimension, a homology theory \piAt_* taking values in A_t(G) based on the homology of the Borel construction, and a finite Adams spectral sequence Ext_{A_t(G)}^{,}(\piAt_*(X), \piAt_(Y)) ==> [X,Y]^G_ for rational G-spectra X and Y.