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

Francis Clarke; Martin Crossley; Sarah Whitehouse

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

Francis Clarke·Martin Crossley·Sarah Whitehouse

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Abstract

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.

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Francis Clarke, Martin Crossley, Sarah Whitehouse. 2006-03-02. The discrete module category for the ring of K-theory operations. https://arxiv.org/abs/math/0603045

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