The generalized homology of products

Mark Hovey 
Wesleyan University   
mhovey@wesleyan.edu   

We construct a spectral sequence that computes the E-homology of a
product of spectra.  The E_{2}-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 (with a
horizontal vanishing line at E_{infty}) when E is the Johnson-Wilson
theory E(n) and each factor of the product is L_{n}-local.  We are able to
prove some results about the E_{2}-term of this spectral sequence; in
particular, we show that the E(n)-homology of a product of
E(n)-module spectra X^{\alpha} is just the comodule product of the
E(n)_{*}X^{\alpha}.  This spectral sequence is relevant to the
chromatic splitting conjecture.