Motivic Birational Covers and Finite Filtrations on Chow Groups

TL;DR

This paper explores decomposing motivic cohomology into smaller parts to better understand the structure of Chow groups, aligning with conjectural filtrations proposed by Bloch and Beilinson.

Contribution

It introduces a new approach to breaking down motivic cohomology, providing a framework for finite filtrations on Chow groups.

Findings

Proposes a method for motivic decomposition

Establishes connections with Bloch-Beilinson filtrations

Lays groundwork for further structural analysis of Chow groups

Abstract

The main goal of this paper is to break up motivic cohomology into smaller pieces as suggested by the conjectural Bloch-Beilinson filtrations for the Chow groups.