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

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

2006-06-21

arxiv.org/abs/math/0606513v3

Acta Math. 200 (2008), no. 2, 155--179.

Mathematics

K-Theory and Homology

Updated final version. Small change in definition of S' construction and correction to the proof of 2.9

Scientific paper

10.1007/s11511-008-0025-4

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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