Comodules and Landweber exact homology theories

We show that, if E is a commutative MU-algebra spectrum such that E-* is Landweber exact over MU, then the category of E*E-comodules is equivalent to a localization of the category of MU*MU-comodules. This localization depends only on the heights of E at the integer primes p. It follows, for example, that the category of E(n)(*)E(n)-comodules is equivalent to the category of (v(n)(-1) BP)(*)(v(n)(-1) BP)-comodules. These equivalences give simple proofs and generalizations of the Miller-Ravenel and Morava change of rings theorems. We also deduce structural results about the category of E*E-comodules. We prove that every E*E-comodule has a primitive, we give a classification of invariant prime ideals in E-*, and we give a version of the Landweber filtration theorem. (c) 2004 Elsevier Inc. All rights reserved.