Separable extensions of noetherian rings and finite étale morphisms of noetherian schemes give rise to separable extensions of singularity categories.
Mac Lane,Categories for the working mathematician, second edition, Graduate Texts in Mathematics, 5, Springer, New York
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The singularity category of a separable extension
Separable extensions of noetherian rings and finite étale morphisms of noetherian schemes give rise to separable extensions of singularity categories.