The localization sequence for the algebraic K-theory of topological K-theory, by Andrew J. Blumberg and Michael A. Mandell

We prove a conjecture of Rognes that establishes 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-infty ring spectrum R with the Quillen K-theory of the abelian category of finitely generated pi_{0}R-modules.


Andrew J. Blumberg <blumberg@math.stanford.edu>
Michael A. Mandell <mmandell@indiana.edu>