The localization sequence for the algebraic K-theory of topological K-theory
K-Theory and Homology
2009-09-06 v3 Algebraic Topology
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.
Keywords
Cite
@article{arxiv.math/0606513,
title = {The localization sequence for the algebraic K-theory of topological K-theory},
author = {Andrew J. Blumberg and Michael A. Mandell},
journal= {arXiv preprint arXiv:math/0606513},
year = {2009}
}
Comments
Updated final version. Small change in definition of S' construction and correction to the proof of 2.9