Nisnevich topology with modulus

TL;DR

This paper introduces a new Grothendieck topology on proper modulus pairs to generalize motives beyond the traditional Nisnevich topology, aiming to expand the framework of Voevodsky's theory.

Contribution

It defines a novel topology on proper modulus pairs and proves its properties, extending the classical Nisnevich topology for motives.

Findings

Topology satisfies Nisnevich-like properties

Enables non-homotopy invariant motives

Provides a foundation for generalized motives

Abstract

In Voevodsky's theory of motives, the Nisnevich topology on smooth schemes is used as an important building block. In this paper, we introduce a Grothendieck topology on proper modulus pairs, which will be used to construct a non-homotopy invariant generalization of motives. We also prove that the topology satisfies similar properties to the Nisnevich topology.