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

الأصل · EN

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 XhG. The E₂-term of the descent spectral sequence for π*(XhG) 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.