Journal of Homotopy and Related Structures

, Volume 10, Issue 3, pp 333–346 | Cite as

Existence and uniqueness of \(E_{\infty }\) structures on motivic \(K\)-theory spectra

  • Niko Naumann
  • Markus Spitzweck
  • Paul Arne Østvær
Article
  • 129 Downloads

Abstract

We show that algebraic \({\textit{K}}\)-theory \(\mathsf {KGL}\), the motivic Adams summand \(\mathsf {ML}\) and their connective covers acquire unique \(E_{\infty }\) structures refining naive multiplicative structures in the motivic stable homotopy category. The proofs combine \(\Gamma \)-homology computations and work due to Robinson giving rise to motivic obstruction theory. As an application we employ a motivic to simplicial delooping argument to show a uniqueness result for \(E_\infty \) structures on the \(K\)-theory Nisnevich presheaf of spectra.

Keywords

Motivic homotopy theory \(E_\infty \) structures Algebraic \(K\)-theory 

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Copyright information

© Tbilisi Centre for Mathematical Sciences 2013

Authors and Affiliations

  • Niko Naumann
    • 1
  • Markus Spitzweck
    • 2
  • Paul Arne Østvær
    • 3
  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany
  2. 2.Institut für MathematikUniversität OsnabrückOsnabrückGermany
  3. 3.Department of MathematicsUniversity of OsloOsloNorway

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