In the theory of motives à la Voevodsky, the Nisnevich topology on smooth schemes is used as an important building block. We introduce a Grothendieck topology on proper modulus pairs, which is used to construct a non-homotopy-invariant generalization of motives. We also prove that the topology satisfies similar properties to the Nisnevich topology.
"Nisnevich topology with modulus." Ann. K-Theory 5 (3) 581 - 604, 2020. https://doi.org/10.2140/akt.2020.5.581