Moving Lemma for additive Chow groups and applications

TL;DR

This paper proves a moving lemma for additive higher Chow groups of smooth projective varieties, establishing their contravariance and a CDGA structure, advancing the understanding of their algebraic and geometric properties.

Contribution

It introduces a moving lemma for additive higher Chow groups and demonstrates their contravariance and CDGA structure, which are novel insights in this area.

Findings

Proved the moving lemma for additive higher Chow groups.

Established the contravariance property of these groups.

Constructed a graded-commutative differential graded algebra structure.

Abstract

We prove moving lemma for additive higher Chow groups of smooth projective varieties. As applications, we prove the very general contravariance property of additive higher Chow groups. Using the moving lemma, we establish the structure of graded-commutative differential graded algebra (CDGA) on these groups.