The Stacks project

Definition 36.35.1. Let $f : X \to S$ be a morphism of schemes which is flat and locally of finite presentation. An object $E$ of $D(\mathcal{O}_ X)$ is perfect relative to $S$ or $S$-perfect if $E$ is pseudo-coherent (Cohomology, Definition 20.47.1) and $E$ locally has finite tor dimension as an object of $D(f^{-1}\mathcal{O}_ S)$ (Cohomology, Definition 20.48.1).

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