The discrete module category for the ring of K-theory operations

Clarke, Francis; Crossley, Martin; Whitehouse, Sarah

The discrete module category for the ring of K-theory operations

Authors

Clarke, Francis

Crossley, Martin

Whitehouse, Sarah

Description

We study the category of discrete modules over the ring of degree zero stable operations in p-local complex K-theory. We show that the p-local K-homology of any space or spectrum is such a module, and that this category is isomorphic to a category defined by Bousfield and used in his work on the K-local stable homotopy category (Amer. J. Math., 1985). We also provide an alternative characterisation of discrete modules as locally finitely generated modules.
19 pages