General Motivic Cohomology and Symplectic Orientation

TL;DR

This paper develops a general framework for motivic cohomology, incorporating symplectic orientation, and explores the embedding of effective Chow-Witt motives, advancing the theoretical foundation of algebraic geometry.

Contribution

It introduces a unified approach to motivic cohomology with symplectic orientation and establishes an embedding theorem for effective Chow-Witt motives, expanding the formalism of motivic theories.

Findings

Established a general motivic cohomology framework

Built part of the six operations formalism for motivic cohomology

Proved an embedding theorem for effective Chow-Witt motives

Abstract

In this paper, we present a general approach to establish motivic cohomology and build part of its six operations formalism. Applying this together with symplectic orientation on MW-motivic cohomology, we discuss the embedding theorem of effective Chow-Witt motives.