Suslin's moving lemma with modulus
  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. 
Wataru Kai, Hiroyasu Miyazaki
math.AG math.KT math.NT