The E_2-term of the descent spectral sequence for continuous G-spectra

Daniel G. Davis

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The E_2-term of the descent spectral sequence for continuous G-spectra

Daniel G. Davis

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Abstract

Let {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.

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Daniel G. Davis. 2006-08-11. The E_2-term of the descent spectral sequence for continuous G-spectra. https://arxiv.org/abs/math/0602480

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