We study the mod-
cohomology spectral sequence arising from delooping the Bousfield–Kan cosimplicial space giving the
–nilpotent completion of a
connective spectrum
. Under
good conditions its
–term
is computable as certain nonabelian derived functors evaluated at
as a
module over the Steenrod algebra, and it converges to the cohomology of
.
We provide general methods for computing the
–term,
including the construction of a multiplicative spectral sequence of Serre type for
cofibration sequences of simplicial commutative algebras. Some simple examples are
also considered; in particular, we show that the spectral sequence collapses at
when
is a
suspension spectrum.
Department of Mathematics
Massachusetts Institute of Technology
Building 2, Room 106
%Rm 2-237 this seems to be old office number 77 Massachusetts
Avenue
Cambridge, MA 02139-4307
United States