Suslin's moving lemma with modulus

Abstract

The moving lemma of Suslin (also known as the generic equidimensionality theorem) 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 a modulus version of the isomorphism, in an appropriate pro setting.