Lemma 76.52.4 (0DKR)—The Stacks project

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Part 4: Algebraic Spaces
Chapter 76: More on Morphisms of Spaces
Section 76.52: Relatively perfect objects
Lemma 76.52.4 (cite)

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Lemma 76.52.4. 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. The full subcategory of $D(\mathcal{O}_ X)$ consisting of $Y$-perfect objects is a saturated ¹ triangulated subcategory.

Proof. This follows from Cohomology on Sites, Lemmas 21.45.4, 21.45.6, 21.46.6, and 21.46.8. $\square$

[1] Derived Categories, Definition 13.6.1.

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