# Motives with modulus, I: Modulus sheaves with transfers for non-proper modulus pairs

## TL;DR

This paper introduces a new framework for modulus sheaves with transfers, extending Voevodsky's theory, and lays the groundwork for the broader development of motives with modulus.

## Contribution

It develops a foundational theory of modulus sheaves with transfers, generalizing existing sheaf theories for use in motives with modulus.

## Key findings

- Established a new theory of modulus sheaves with transfers
- Generalized Voevodsky's sheaves with transfers
- Laid groundwork for motives with modulus

## Abstract

We develop a theory of modulus sheaves with transfers, which generalizes Voevodsky's theory of sheaves with transfers. This paper and its sequel are foundational for the theory of motives with modulus, which is developed in [KMSY20].