Existence and uniqueness of E-infinity structures on motivic K-theory spectra

TL;DR

This paper proves the existence and uniqueness of E-infinity structures on motivic K-theory spectra, combining Gamma-homology computations and motivic obstruction theory, with applications to delooping arguments.

Contribution

It establishes the unique E-infinity structures on motivic K-theory spectra and their connective covers, advancing the understanding of multiplicative structures in motivic homotopy theory.

Findings

Unique E-infinity structures on KGL and ML spectra

Application of motivic to simplicial delooping for structure uniqueness

Integration of Gamma-homology and Robinson's work in motivic obstruction theory

Abstract

We show that algebraic K-theory KGL, the motivic Adams summand ML and their connective covers acquire unique E-infinity 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-infinity structures on the K-theory Nisnevich presheaf of spectra.