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

Daniel G. Davis

Published 2006-02-21, updated 2006-08-11Version 2

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 \pi_*(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.

Comments: 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 file
Journal: New York J. of Math. 12 (2006), 183-191
Categories: math.AT
Subjects: 55T05
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