The singularity category of a separable extension

TL;DR

This paper demonstrates that certain algebraic and geometric extensions induce separable extensions in their associated singularity categories, linking ring and scheme theory with category theory.

Contribution

It establishes the connection between separable extensions of rings and schemes and their impact on singularity categories, a novel theoretical insight.

Findings

Separable extensions of noetherian rings induce separable extensions of singularity categories.

Finite étale morphisms of noetherian schemes lead to separable extensions of their singularity categories.

Abstract

We prove that separable extensions of noetherian rings and finite \'etale morphisms of noetherian schemes give rise to separable extensions of singularity categories.