Topologies on schemes and modulus pairs

TL;DR

This paper investigates the connections between the Nisnevich topology on smooth schemes and specific Grothendieck topologies on modulus pairs, advancing the understanding of sheaves with transfers in algebraic geometry.

Contribution

It establishes new relationships between topologies on schemes and modulus pairs, enhancing the theoretical framework for sheaves with transfers on proper modulus pairs.

Findings

Identifies key relationships between Nisnevich and Grothendieck topologies.

Clarifies the role of these topologies in sheaves with transfers.

Provides foundational results for future research in algebraic geometry.

Abstract

We study relationships between the Nisnevich topology on smooth schemes and certain Grothendieck topologies on proper and not necessarily proper modulus pairs which were introduced respectively in [9] and [3]. Our results play an important role in the theory of sheaves with transfers on proper modulus pairs. This is a revised version of arXiv:1809.05851 [math.AG].