  We show that the category of rational G-spectra for a torus G is Quillen
equivalent to an explicit small and practical algebraic model, thereby
providing a universal de Rham model for rational G-equivariant cohomology
theories. The result builds on the first author's Adams spectral sequence, the
second author's functors making rational spectra algebraic.
  There are several steps, some perhaps of wider interest (1) isotropy
separation (replacing the category of G-spectra by modules over a diagram of
isotropically simple ring G-spectra) (2) passage to fixed points on ring and
module categories (replacing diagrams of ring G-spectra by diagrams of ring
spectra) (3) replacing diagrams of ring spectra by diagrams of differential
graded algebras (4) rigidity (replacing diagrams of DGAs by diagrams of graded
rings). Systematic use of cellularization of model categories is central.
