### Explicit fibrant replacement for discrete G-spectra, by Daniel G. Davis

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.

Daniel G. Davis <dgdavis@louisiana.edu>