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Convergence of the homology spectral sequence of a cosimplicial space

We produce new convergence conditions for the homology spectral sequence of a cosimplicial space by requiring that each codegree of the cosimplicial space has finite type mod p homology. Specifically, we find conditions which ensure strong convergence if and only if the total space has p-good components. We also find exotic convergence conditions for cosimplicial spaces not covered by the strong convergence conditions. These results give new convergence conditions, for example, for the Eilenberg-Moore spectral sequence and for mapping spaces.