The localization sequence for the algebraic <Emphasis Type="Italic">K</Emphasis>-theory of topological <Emphasis Type="Italic">K</Emphasis>-theory |
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Authors: | Andrew J Blumberg Michael A Mandell |
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Institution: | 1.Department of Mathematics,Stanford University,Stanford,USA;2.Department of Mathematics,Indiana University,Bloomington,USA |
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Abstract: | We verify a conjecture of Rognes by establishing a localization cofiber sequence of spectra \(K(\mathbb{Z})\to K(ku)\to K(KU) \to\Sigma K(\mathbb{Z})\) for the algebraic K-theory of topological K-theory. We deduce the existence of this sequence as a consequence of a dévissage theorem identifying the K-theory of the Waldhausen category of finitely generated finite stage 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. |
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