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, At(G) of finite injective dimension, a homology theory π⁎At(⋅) taking values in At(G) based on the homology of the Borel construction, and a finite Adams spectral sequenceExtAt(G)⁎,⁎(π⁎At(X),π⁎At(Y))⇒[X,Y]⁎G for rational G-spectra X and Y.