MW-motivic complexes

TL;DR

This paper develops a new theory of motivic complexes based on cycles with quadratic form coefficients, aligning more closely with $ ext{A}^1$-homotopy theory than previous approaches.

Contribution

It introduces a motivic complex framework using cycles and correspondences with quadratic form coefficients, offering a perspective closer to $ ext{A}^1$-homotopy theory.

Findings

New framework for motivic complexes based on quadratic forms

Closer alignment with $ ext{A}^1$-homotopy theory

Potential for new insights in algebraic geometry

Abstract

The aim of this work is to develop a theory parallel to that of motivic complexes based on cycles and correspondences with coefficients in quadratic forms. This framework is closer to the point of view of $\mathbb{A}^1$-homotopy than the original one envisioned by Beilinson and set up by Voevodsky.