Comodules and Landweber exact homology theories
Mark Hovey and Neil Strickland
Wesleyan University University of Sheffield
mhovey@wesleyan.edu N.P. Strickland@sheffield.ac.uk
We show that, if E is a Landweber exact ring spectrum, then the category
of E_*E-comodules is equivalent to the localization of the category of
BP_*BP-comodules with respect to the hereditary torsion theory of
v_n-torsion comodules, where n is the height of E. In particular, the
category of E(n)_*E(n)-comodules is equivalent to the category of
(v_n^{-1}BP)_*(v_n^{-1}BP)-comodules. We also prove structure theorems
for E_*E-comodules; we show every E_*E-comodule has a primitive, we
classify the invariant radical ideals, and we prove a version of the
Landweber filtration theorem.