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


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.


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



The main result of this paper was announced by the first named author at the 2009 Münster workshop on Motivic Homotopy Theory. He thanks the organizers E. M. Friedlander, G. Quick and P. A. Østvær for the invitation, and P. A. Østvær for hospitality while visiting the University of Oslo, where the major part of this work was finalized. The authors thank A. Robinson for valuable discussions keeping us informed about his recent work, an anonymous referee and J. Rognes for comments on a shorter version of this paper and another referee for a careful inspection of the final section.


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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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