New York Journal of Mathematics Volume 12 (2006) 183-191
 Volume 12

Daniel G. Davis

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

 Published: August 2, 2006 Keywords: Homotopy fixed point spectrum, descent spectral sequence, continuous G-spectrum Subject: 55P42, 55T99

Abstract
Given a profinite group G with finite virtual cohomological dimension, 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 \pi(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.

Acknowledgements

The author was partially supported by an NSF grant. Most of this paper was written during a visit to the Institut Mittag-Leffler (Djursholm, Sweden).

Author information

Department of Mathematics, Purdue University, 150 N. University St., W. Lafayette, IN, 47907
dgdavis@math.purdue.edu