Chromatic phenomena in the algebra of BP_{*}BP-comodules

Mark Hovey
Wesleyan University 
mhovey@wesleyan.edu 

This paper begins with an exposition of the author's research on the
category of BP_*BP-comodules, much of which is joint with Neil
Strickland.  We give an overview of the results obtained in the papers
Hovey/comodule, Hovey-Strickland/torsion-comod, and
Hovey-Strickland/derived-ln.  The main result of that work is that the
category of E(n)_*E(n)-comodules is equivalent to a localization of the
category of BP_*BP-comodules (the localization is L_n, analogous to the
topological L_n).  

The main new result in this paper is that, analogously, the stable
homotopy category of E(n)_*E(n)-comodules is equivalent to a
localization (the finite localization L_n^f this time, not L_n) of the
stable homotopy category of BP_*BP-comodules.  These stable homotopy
categories were constructed in Hovey/comodule, and are supposed to model
stable homotopy theory; it is like stable homotopy theory where there
are no differentials in the Adams-Novikov spectral sequence.  Our result
embeds the Miller-Ravenel and Hovey-Sadofsky change of rings theorems
as special cases of isomorphisms like

[X,Y]=[L_n^f X, Y]

for L_n^f-local objects Y.