#
Epimorphic covers make $R^+_G$ a site, for profinite $G$

##
Daniel G. Davis

Let $G$ be a non-finite profinite group and let $G-Sets_{df}$ 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
$G-Sets_{df}$ 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.

Keywords:
site, profinite group, finite discrete $G$-sets, presheaves of spectra,
Lubin-Tate spectrum, continuous $G$-spectrum

2000 MSC:
55P42, 55U35, 18B25

*Theory and Applications of Categories,*
Vol. 22, 2009,
No. 16, pp 388-400.

http://www.tac.mta.ca/tac/volumes/22/16/22-16.dvi

http://www.tac.mta.ca/tac/volumes/22/16/22-16.ps

http://www.tac.mta.ca/tac/volumes/22/16/22-16.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/16/22-16.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/16/22-16.ps

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/16/22-16.pdf

Revised 2009-10-05. Original version at

http://www.tac.mta.ca/tac/volumes/22/16/22-16a.dvi

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