## Homology, Homotopy and Applications

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

David Barnes

#### 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.

#### Article information

Source
Homology Homotopy Appl., Volume 11, Number 1 (2009), 141-170.

Dates
First available in Project Euclid: 1 September 2009

https://projecteuclid.org/euclid.hha/1251832563

Mathematical Reviews number (MathSciNet)
MR2506130

Zentralblatt MATH identifier
1163.55003

Keywords
Equivariant cohomology

#### Citation

Barnes, David. Classifying rational $G$-spectra for finite $G$. Homology Homotopy Appl. 11 (2009), no. 1, 141--170. https://projecteuclid.org/euclid.hha/1251832563