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...