Convergence of the homology spectral sequence of a cosimplicial space

ABSTRACT. By adding finite type homology conditions we generalize previous convergence conditions due to Bousfield for the homology spectral sequence of a cosimplicial space. This generalization was motivated by a special case due to Lannes in his work on the Sullivan conjecture. We also generalize Dwyer's exotic convergence results for the classical Eilenberg-Moore spectral sequence of a fibration.