Lemma 36.35.4. Let $f : X \to S$ be a morphism of schemes which is flat and locally of finite presentation. The full subcategory of $D(\mathcal{O}_ X)$ consisting of $S$-perfect objects is a saturated^{1} triangulated subcategory.

**Proof.**
This follows from Cohomology, Lemmas 20.44.4, 20.44.6, 20.45.6, and 20.45.8.
$\square$

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