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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