Geodesic
Explicit fibrant replacement for discrete $G$-spectra
Homology, homotopy, and applications, Tome 10 (2008) no. 3, pp. 137-150.

Voir la notice de l'article provenant de la source International Press of Boston

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 $G$.
DOI : 10.4310/HHA.2008.v10.n3.a7
Classification : 55P42, 55P91
Keywords: homotopy fixed points, discrete $G$-spectrum, homotopy limit 
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Daniel G. Davis. Explicit fibrant replacement for discrete $G$-spectra. Homology, homotopy, and applications, Tome 10 (2008) no. 3, pp. 137-150. doi : 10.4310/HHA.2008.v10.n3.a7. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n3.a7/

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