Finite Chow-Witt correspondences

TL;DR

This paper introduces finite Chow-Witt correspondences over a perfect field and explores their role in defining generalized motivic cohomology groups, linking them to traditional motivic cohomology.

Contribution

It develops the category of finite Chow-Witt correspondences and initiates the study of their connection to classical motivic cohomology.

Findings

Defined bigraded generalized motivic cohomology groups

Established initial links with ordinary motivic cohomology

Provided a new categorical framework for motivic theories

Abstract

We introduce the category of finite Chow-Witt correspondences over a perfect field k of characteristic not 2. We then use them to define bigraded generalized motivic cohomology groups of a smooth scheme over k and begin the study of their relationship with ordinary motivic cohomology groups.