Definition 76.52.1. Let S be a scheme. Let f : X \to Y be a morphism of algebraic spaces over S which is flat and locally of finite presentation. An object E of D(\mathcal{O}_ X) is perfect relative to Y or Y-perfect if E is pseudo-coherent (Cohomology on Sites, Definition 21.45.1) and E locally has finite tor dimension as an object of D(f^{-1}\mathcal{O}_ Y) (Cohomology on Sites, Definition 21.46.1).
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