 

Daniel G. Davis
The E_{2}term of the descent spectral sequence for continuous Gspectra


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


Abstract
Given a profinite group G with finite virtual cohomological dimension,
let {X_{i}} be a tower of discrete Gspectra, each of which is
fibrant as a spectrum, so that X=holim_{i} X_{i} is a continuous Gspectrum,
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 Gmodules.


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


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

