Proper base change for separated locally proper maps

TL;DR

This paper extends key sheaf theory concepts like proper base change, projection formula, and Verdier duality to separated locally proper maps between arbitrary topological spaces, broadening their applicability beyond locally compact Hausdorff spaces.

Contribution

It introduces the notion of a locally proper map and generalizes fundamental sheaf theory constructions to this broader class of maps.

Findings

Proper base change holds for separated locally proper maps.

Projection formula extends to these maps.

Verdier duality is applicable in this setting.

Abstract

We introduce and study the notion of a locally proper map between topological spaces. We show that fundamental constructions of sheaf theory, more precisely proper base change, projection formula, and Verdier duality, can be extended from continuous maps between locally compact Hausdorff spaces to separated locally proper maps between arbitrary topological spaces.