The site R+G for a profinite group G

الأصل · EN

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.