Suslin's moving lemma with modulus
Wataru Kai, Hiroyasu Miyazaki
The moving lemma of Suslin states that a cycle on $X \times \mathbb{A}^1$ meeting all faces properly can be moved so that it becomes equidimensional over $X \times \mathbb{A}^1$. 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.
Reference : Annals of K-theory 10.2140/akt.2018.3.55
ArXiv link : https://arxiv.org/abs/1604.04356