Finiteness of global dimension relative to compact silting objects is intrinsic to the triangulated category and independent of the silting object chosen.
Keller , Calabi-Yau triangulated categories Trends in representation theory of algebras and related topics, 467–489
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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.