Chromatic Phenomena in the Algebra of Bp∗bp -comodules

We describe the author’s research with Neil Strickland on the global algebra and global homological algebra of the category of BP∗BP comodules. We show, following [HS02a], that the category of E(n)∗E(n)comodules is a localization, in the abelian sense, of the category of BP∗BP comodules. This gives analogues of the usual structure theorems, such as the Landweber filtration theorem, for E(n)∗E(n)-comodules. We recall the work of [Hov02a], where an improved version Stable(Γ) of the derived category of comodules over a well-behaved Hopf algebroid (A,Γ) is constructed. The main new result of the paper is that Stable(E(n)∗E(n)) is a Bousfield localization of Stable(BP∗BP ), in analogy to the abelian case.