The homotopy orbit spectrum for profinite groups

Details The homotopy orbit spectrum for profinite groups The homotopy orbit spectrum for profinite groups

2006-08-10

arxiv.org/abs/math/0608262v1

Mathematics

Algebraic Topology

13 pages

Scientific paper

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 $\hat{\mathbb{Z}}[[G]]$-module $\pi_\ast(X)$. 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.

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