Separable extensions preserve finiteness of global dimension, Gorensteinness and regularity in compactly generated triangulated categories while relating their singularity categories up to retracts.
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Separable extensions of noetherian rings and finite étale morphisms of noetherian schemes give rise to separable extensions of singularity categories.
Finiteness of global dimension relative to compact silting objects is intrinsic to the triangulated category and independent of the silting object chosen.
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Homological Aspects of Separable Extensions of Triangulated Categories
Separable extensions preserve finiteness of global dimension, Gorensteinness and regularity in compactly generated triangulated categories while relating their singularity categories up to retracts.
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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.
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Global dimension of dg algebras via compact silting objects
Finiteness of global dimension relative to compact silting objects is intrinsic to the triangulated category and independent of the silting object chosen.