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# Homology, Homotopy and Applications

## Volume 11 (2009)

### Number 1

### Classifying rational $G$-spectra for finite $G$

Pages: 141 – 170

DOI: http://dx.doi.org/10.4310/HHA.2009.v11.n1.a7

#### Author

#### Abstract

We give a new proof that for a finite group $G$, the category of rational $G$-equivariant spectra is Quillen equivalent to the product of the model categories of chain complexes of modules over the rational group ring of the Weyl group of $H$ in $G$, as $H$ runs over the conjugacy classes of subgroups of $G$. Furthermore, the Quillen equivalences of our proof are all symmetric monoidal. Thus we can understand categories of algebras or modules over a ring spectrum in terms of the algebraic model.

#### Keywords

equivariant cohomology

#### 2010 Mathematics Subject Classification

55N91, 55P42