The Generalized Homology of Products

We construct a spectral sequence that computes the generalized homology E∗( Q Xα) of a product of spectra. The E2-term of this spectral sequence consists of the right derived functors of product in the category of E∗E-comodules, and the spectral sequence always converges when E is the Johnson-Wilson theory E(n) and the Xα are Ln-local. We are able to prove some results about the E2-term of this spectral sequence; in particular, we show that the E(n)-homology of a product of E(n)-module spectra Xα is just the comodule product of the E(n)∗X. This spectral sequence is relevant to the chromatic splitting conjecture.