Title: The homotopy orbit spectrum for profinite groups
Author: Daniel G. Davis
Author's e-mail address: dgdavis@math.purdue.edu
Abstract: Let G be a profinite group. We define an S[[G]]-module to be a
G-spectrum X that satisfies certain conditions, and, given an
S[[G]]-module X, we define the homotopy orbit spectrum X_{hG}. When G is
countably based and X satisfies a certain finiteness condition, we
construct a homotopy orbit spectral sequence whose E_2-term is the
continuous homology of G with coefficients in the graded profinite
Z[[G]]-module pi_*X. Let G_n be the extended Morava stabilizer group and
let E_n be the Lubin-Tate spectrum. As an application of our theory, we
show that the function spectrum F(E_n,L_{K(n)}(S^0)) is an
S[[G_n]]-module with an associated homotopy orbit spectral sequence.