Suslin's moving lemma with modulus

TL;DR

This paper extends Suslin's moving lemma to a modulus setting, establishing an isomorphism between Suslin homology with modulus and higher Chow groups with modulus in a pro context.

Contribution

It formulates and proves a variant of Suslin's moving lemma incorporating modulus conditions, linking Suslin homology with modulus to higher Chow groups with modulus.

Findings

Established an isomorphism between Suslin homology with modulus and higher Chow groups with modulus.

Extended Suslin's moving lemma to include modulus conditions.

Proved the variant in an appropriate pro setting.

Abstract

The moving lemma of Suslin states that a cycle on $X\times \mathbb{A} ^n$ meeting all faces properly can be moved so that it becomes equidimensional over $\mathbb{A}^n$. This leads to an isomorphism of motivic Borel-Moore homology and higher Chow groups. In this short paper we formulate and prove a variant of this. It leads to an isomorphism of Suslin homology with modulus and higher Chow groups with modulus, in an appropriate pro setting.