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

By Andrew Justin Blumberg, Michael A. Mandell. Acta Mathematica, 2006

70 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/87507ff3a5e03259bb0a191fec38011a6fb243f9

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The Local Structure of Algebraic K-Theory (2012, background): “In particular, in [22] Blumberg and Mandell show that there is a fiber sequence K(HZ)→ K(ku)→ K(KU) where the first map is a transfer-type homomorphism similar to the inclusion of the category of finite abelian groups into the category of finitely generated abelian groups, and where the last map is ”
On the algebraic K‐theory of higher categories (2012, methodology): “Of course, when n = 1, such a Dévissage Theorem has already been provided thanks to beautiful work of Andrew Blumberg and Mike Mandell [15].”