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The localization sequence for the algebraic K-theory of topological K-theory

Andrew J. Blumberg·Michael A. Mandell
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Abstract

We prove a conjecture of Rognes by establishing a localization cofiber sequence of spectra, K(Z) to K(ku) to K(KU) to Sigma K(Z), for the algebraic K-theory of topological K-theory. We deduce the existence of this sequence as a consequence of a devissage theorem identifying the K-theory of the Waldhausen category of Postnikov towers of modules over a connective A-infinity ring spectrum R with the Quillen K-theory of the abelian category of finitely generated pi_0(R)-modules.

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BibTeXRIS

Andrew J. Blumberg, Michael A. Mandell. 2007-08-31. The localization sequence for the algebraic K-theory of topological K-theory. https://doi.org/10.1007/s11511-008-0025-4

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