Normed motivic spectra and power operations

TL;DR

This paper develops power operations for normed motivic spectra using motivic colimits, demonstrating that the motivic dual Steenrod algebra is generated by a single element under these operations, akin to classical results.

Contribution

It introduces a construction of power operations on homotopy groups of normed motivic spectra and proves a motivic analog of Steinberger's theorem.

Findings

Motivic dual Steenrod algebra is generated by one element under ring and power operations.

Constructs power operations on homotopy groups of normed motivic spectra.

Establishes properties of these power operations in the motivic setting.

Abstract

We use motivic colimits to construct power operations on the homotopy groups of normed motivic spectra admitting a (normed) map from HF_2. We establish enough of their standard properties to prove that the motivic dual Steenrod algebra is generated by one element under ring and power operations, establishing a motivic analog of Steinberger's theorem.