On the generalisation of cohomology with compact support to non-finite type schemes

TL;DR

This paper extends the framework of cohomology with compact support to a broader class of schemes, including non-finite type schemes, by generalizing Deligne's construction of Grothendieck's six operations.

Contribution

It introduces a new extension of cohomological tools to non-finite type schemes, broadening the applicability of étale cohomology theories.

Findings

Successfully extends Grothendieck's six operations to non-finite type schemes.

Includes profinite étale coverings and separated morphisms of finite type.

Provides a foundation for further research in cohomology of more general schemes.

Abstract

In this article we extend Deligne's construction of Grothendieck's six operations on the derived category of torsion sheaves over the \'etale site of a scheme for morphisms of finite type to a larger class of morphisms. This class includes profinite \'etale coverings as well as separated morphisms perfectly of finite type