An algebraic model for rational S^1-equivariant stable homotopy theory
Brooke Shipley

Abstract. Greenlees defined an abelian category \mathcal A whose derived
category is equivalent to the rational S^1-equivariant stable homotopy
category whose objects represent rational S^1-equivariant cohomology theories.
We show that in fact the model category of differential graded objects in
\mathcal A models the whole rational S^1-equivariant stable homotopy theory.
That is, we show that there is a Quillen equivalence between dg\mathcal A
and the model category of rational S^1-equivariant spectra, before the
quasi-isiomorphisms or stable equivalences have been inverted. This implies
that all of the higher order structures such as mapping spaces, function
spectra and homotopy (co)limits are reflected in the algebraic model.