Reduced power operations in motivic cohomology

TL;DR

This paper develops an analog of Steenrod operations within motivic cohomology, establishing their fundamental properties and relations to characteristic classes, advancing the algebraic topology toolkit for motivic settings.

Contribution

It introduces and proves the basic properties of Steenrod operations in motivic cohomology, a novel extension of classical cohomology operations.

Findings

Constructed motivic Steenrod operations.

Proved Cartan formula and Adem relations for these operations.

Established connections to characteristic classes.

Abstract

In this paper we construct an analog of Steenrod operations in motivic cohomology and prove their basic properties including the Cartan formula, the Adem relations and the realtions to characteristic classes.