The Site R G for a Profinite Group 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. Also, we explain why the associated topology on R G is not subcanonical, and hence, not canonical. We note that, since R G is a site, there is automatically a model category structure on the category of presheaves of spectra on the site. Finally, we point out that such presheaves of spectra are a nice 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.