Morava E-theory is n-1 derived functors away from a homology theory
Mark Hovey
Wesleyan University
mhovey@wesleyan.edu
Morava E-theory E_{n*}^{\vee }(-) is a much-studied theory in algebraic
topology, but it is not a homology theory in the usual sense, because it
fails to preserve coproducts. The object of this paper is to construct
a spectral sequence to compute the Morava E-theory of a coproduct or a
filtered homotopy colimit. The E_{2} term of this spectral sequence
involves the derived functors of direct sum or filtered colimit in an
appropriate abelian category. We show that there are at most n-1 of
these derived functors, (n in the filtered colimit case), whence the
title of the paper. When n=1, it follows that homotopy commutes with an
appropriate version of direct sum in the K(1)-local stable homotopy
category.