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.
"On a spectral sequence for the cohomology of infinite loop spaces." Algebr. Geom. Topol. 16 (5) 2911 - 2947, 2016. https://doi.org/10.2140/agt.2016.16.2911