The derived category of an \'etale extension and the separable Neeman-Thomason theorem

TL;DR

This paper demonstrates that etale morphisms induce separable extensions in derived categories and extends the Neeman-Thomason Localization Theorem to these separable extensions of triangulated categories.

Contribution

It establishes a link between etale morphisms and separable extensions in derived categories and generalizes a key localization theorem to this context.

Findings

Etale morphisms induce separable extensions of derived categories.

The Neeman-Thomason Localization Theorem is extended to separable extensions.

Provides a new framework for understanding derived categories of schemes.

Abstract

We prove that etale morphisms of schemes yield separable extensions of derived categories. We then generalize the Neeman-Thomason Localization Theorem to separable extensions of triangulated categories.