Homology, Homotopy and Applications
Volume 10 (2008)
Proceedings of a Conference in Honor of Douglas C. Ravenel and W. Stephen Wilson
Explicit fibrant replacement for discrete $G$-spectra
Pages: 137 – 150
If $C$ is the model category of simplicial presheaves on a site with enough points, with fibrations equal to the global fibrations, then it is well-known that the fibrant objects are, in general, mysterious. Thus, it is not surprising that, when $G$ is a profinite group, the fibrant objects in the model category of discrete $G$-spectra are also difficult to get a handle on. However, with simplicial presheaves, it is possible to construct an explicit fibrant model for an object in $C$, under certain finiteness conditions. Similarly, in this paper, we show that if $G$ has finite virtual cohomological dimension and $X$ is a discrete $G$-spectrum, then there is an explicit fibrant model for $X$. Also, we give several applications of this concrete model related to closed subgroups of $G$.
homotopy fixed points; discrete $G$-spectrum; homotopy limit
2010 Mathematics Subject Classification