Homology, Homotopy and Applications

Volume 11 (2009)

Number 1

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

Pages: 141 – 170

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


David Barnes (Department of Mathematics, The University of Western Ontario, London, Ontario, Canada)


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.


equivariant cohomology

2010 Mathematics Subject Classification

55N91, 55P42

Published 1 January 2009