I am trying to learn about the Eilenberg-Moore spectral sequence to compute homology and cohomology. I have been using Hatcher's book on spectral sequences and also McCleary's "A User's Guide to Spectral Sequences" but I am confused about the convergence of the sequence if we take coefficients in a ring, such as the integers, rather than a field. The two texts seem to use coefficients over a field.

Does the spectral sequence converge if we take ring coefficients?

  • $\begingroup$ maybe the problem is not the convergence, but rather that we do not have an isomorphism: $$ \bigoplus_{p+q=n} E^r_{p, q} \sim H_n(E) $$ where $E$ is the total space of some fibration, the coefficients are in the relevant ring, and $r$ is sufficiently large. In case the ring is a field, we always have such isomorphism, if the sequence converges $\endgroup$ – fritz Jan 31 '17 at 15:21

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