Robert R. BRUNER (Wayne State U.): Idempotents, Localizations and Picard groups of A(1)-modules

If B is a sub-Hopf algebra of the mod 2 Steenrod algebra, the category of B-modules has subcategories of modules local or colocal with respect to certain Margolis homologies, and corresponding localization and colocalization functors. The Picard groups of these subcategories are sufficient to detect the Picard group of the whole category and contain modules of geometric interest. General results obtained along the way allow us to begin to attack the analogous questions for E(2) and A(2)-modules. Applications include better descriptions of polynomial algebras as modules over the Steenrod algebra, and of the values of certain generalized cohomology theories on the classifying spaces of elementary abelian groups.