The localization sequence for the algebraic K-theory of topological K-theory
AJ Blumberg, MA Mandell - 2008 - projecteuclid.org
2008•projecteuclid.org
We verify a conjecture of Rognes by establishing a localization cofiber sequence of spectra
K(Z)→K(ku)→K(KU)→ΣK(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_∞ ring spectrum R with the Quillen K-theory of the abelian
category of finitely generated 0R-modules.
K(Z)→K(ku)→K(KU)→ΣK(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_∞ ring spectrum R with the Quillen K-theory of the abelian
category of finitely generated 0R-modules.
Abstract
We verify a conjecture of Rognes by establishing a localization cofiber sequence of spectra 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 ring spectrum R with the Quillen K-theory of the abelian category of finitely generated -modules.
Project Euclid以上显示的是最相近的搜索结果。 查看全部搜索结果