An Algebraic Model For Free Rational G-Spectra for Connected Compact Lie Groups G.

We show that the category of free rational G-spectra for a connected compact Lie group G is Quillen equivalent to the category of torsion differential graded modules over the polynomial ring H∗(BG). The ingredients are the enriched Morita equivalences of [30], the functors of [34] making rational spectra algebraic and Koszul duality and thick subcategory arguments based on the simplicity of the derived category of a polynomial ring.