The E2-term of the descent spectral sequence for continuous G-spectra

Given a profinite group G with finite virtual cohomological dimen- sion, let {Xi} be a tower of discrete G-spectra, each of which is fibrant as a spectrum, so that X = holimi Xi is a continuous G-spectrum, with homotopy fixed point spectrum X hG . The E2-term of the descent spectral sequence for π∗(X hG ) cannot always be expressed as continuous cohomology. However, we show that the E2-term is always built out of a certain complex of spectra, that, in the context of abelian groups, is used to compute the continuous cochain cohomology of G with coefficients in limi Mi, where {Mi} is a tower of discrete G-modules.