Trace formalism for motivic cohomology

TL;DR

This paper develops a trace formalism for motivic cohomology, extending it to an $$-enhanced setting using functorial reinterpretations, advancing the theoretical framework of motivic cohomology.

Contribution

It constructs trace maps for the six functor formalism in motivic cohomology and introduces an $$-enhancement using Suslin-Voevodsky's cycle groups, providing a more functorial approach.

Findings

Constructed trace maps for motivic cohomology formalism.

Developed an $$-enhancement of the trace formalism.

Reinterpreted the formalism using Suslin-Voevodsky cycle groups.

Abstract

The goal of this paper is to construct trace maps for the six functor formalism of motivic cohomology after Voevodsky, Ayoub, and Cisinski-D\'{e}glise. We also construct an $\infty$-enhancement of such a trace formalism. In the course of the $\infty$-enhancement, we need to reinterpret the trace formalism in a more functorial manner. This is done by using Suslin-Voevodsky's relative cycle groups.