Comodules and Landweber exact homology theories
By Mark Hovey, N. Strickland. 2003
58 citations recorded by the source corpus.
Abstract 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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0c82975c43887ecbcecc95ef760730560274c926
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Citations in the corpus
- The stack of formal groups in stable homotopy theory (2007, methodology): “1 of [15] we define the height of φ to be ht(φ) := max{N 0 | R/INR = 0} which may be ∞ and we agree to put ht(φ) := −1 in case R = 0, i.”