A moving lemma for algebraic cycles with modulus and contravariance

TL;DR

This paper establishes a moving lemma for algebraic cycles with modulus, demonstrating contravariance properties of certain higher Chow groups in smooth varieties using novel translation techniques.

Contribution

It introduces a new moving lemma involving parallel translation with modulus and Noether's normalization, enabling contravariance of additive higher Chow groups.

Findings

Contravariance of Bloch-Esnault's additive higher Chow group in smooth affine varieties.

Contravariance of Binda-Saito's higher Chow group in smooth varieties with Cartier divisors.

Introduction of a new moving method using parallel translation with modulus.

Abstract

We prove a moving lemma which implies the contravariance of Bloch-Esnault's additive higher Chow group in smooth affine varieties and Binda-Saito's higher Chow group (taken in the Nisnevich topology) in smooth varieties equipped with effective Cartier divisors. The new ingredients in the moving method are parallel translation {\em with modulus} in the affine space that involves a new integer parameter, and Noether's normalization lemma over a Dedekind base.