Lemma 36.35.6. Let f : X \to S be a morphism of schemes which is flat and locally of finite presentation. Let g : S' \to S be a morphism of schemes. Set X' = S' \times _ S X and denote g' : X' \to X the projection. If K \in D(\mathcal{O}_ X) is S-perfect, then L(g')^*K is S'-perfect.
Proof. First proof: reduce to the affine case using Lemma 36.35.3 and then apply More on Algebra, Lemma 15.83.5.
Second proof: L(g')^*K is pseudo-coherent by Cohomology, Lemma 20.47.3 and the bounded tor dimension property follows from Lemma 36.22.8. \square
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