## Homology, Homotopy and Applications

- Homology Homotopy Appl.
- Volume 10, Number 3 (2008), 137-150.

### Explicit fibrant replacement for discrete G-spectra

#### Abstract

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 $G$.

#### Article information

**Source**

Homology Homotopy Appl., Volume 10, Number 3 (2008), 137-150.

**Dates**

First available in Project Euclid: 1 September 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.hha/1251832470

**Mathematical Reviews number (MathSciNet)**

MR2475620

**Zentralblatt MATH identifier**

1178.55009

**Subjects**

Primary: 55P42: Stable homotopy theory, spectra 55P91: Equivariant homotopy theory [See also 19L47]

**Keywords**

Homotopy fixed points discrete G-spectrum homotopy limit

#### Citation

Davis, Daniel G. Explicit fibrant replacement for discrete G-spectra. Homology Homotopy Appl. 10 (2008), no. 3, 137--150. https://projecteuclid.org/euclid.hha/1251832470