Epimorphic Covers Make R + G a Site , for Profinite G

Let G be a non-finite profinite group and let G−Setsdf be the canonical site of finite discrete G-sets. Then the category R G, defined by Devinatz and Hopkins, is the category obtained by considering G−Setsdf together with the profinite G-space G itself, with morphisms being continuous G-equivariant maps. We show that R G is a site when equipped with the pretopology of epimorphic covers. We point out that presheaves of spectra on R G are an efficient way of organizing the data that is obtained by taking the homotopy fixed points of a continuous G-spectrum with respect to the open subgroups of G. Additionally, utilizing the result that R G is a site, we describe various model category structures on the category of presheaves of spectra on R G and make some observations about them.