A Lyndon-Hochschild-Serre spectral sequence for certain homotopy fixed point spectra

Abstract:

Let $H$ and $K$ be closed subgroups of the extended Morava stabilizer group $G_n$ and suppose that $H$ is normal in $K$. We construct a strongly convergent spectral sequence \[ H^\ast _c(K/H, (E^{hH}_n)^\ast X) \Rightarrow (E^{hK}_n)^\ast X, \] where $E^{hH}_n$ and $E^{hK}_n$ are the continuous homotopy fixed point spectra of Devinatz and Hopkins. This spectral sequence turns out to be an Adams spectral sequence in the category of $K(n)_\ast$-local $E^{hK}_n$-modules.