2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/109062Let {X_i} be a tower of discrete G-spectra, each of which is fibrant as a spectrum, so that X=holim_i X_i is a continuous G-spectrum, with homotopy fixed point spectrum X^{hG}. The E_2-term of the descent spectral sequence for π_*(X^{hG}) cannot always be expressed as continuous cohomology. However, we show that the E_2-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 lim_i M_i, where {M_i} is a tower of discrete G-modules.8 pages. Main result simplified. Expository Section 3 added. Error in Definition 2.1 is repaired. Same as published version, except for changes required by journal's style fileAlgebraic Topology55T05text