On the motivic Peterson conjecture

TL;DR

This paper demonstrates that the Peterson conjecture, concerning Steenrod squares, does not extend to motivic cohomology, challenging previous assumptions in algebraic topology.

Contribution

It provides the first counterexample showing the conjecture fails in the motivic setting, highlighting differences from classical cohomology.

Findings

The motivic analogue of the Peterson conjecture does not hold.

Counterexamples show the conjecture's failure in motivic cohomology.

The result impacts the understanding of Steenrod operations in motivic contexts.

Abstract

We show that the analogue of the Peterson conjecture on the action of Steenrod squares does not hold in motivic cohomology.