Lemma 20.49.9 (08CS)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 20: Cohomology of Sheaves
Section 20.49: Perfect complexes
Lemma 20.49.9 (cite)

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Lemma 20.49.9. Let $(X, \mathcal{O}_ X)$ be a ringed space. If $K \oplus L$ is a perfect object of $D(\mathcal{O}_ X)$, then so are $K$ and $L$.

Proof. Follows from Lemmas 20.49.5, 20.47.6, and 20.48.8. $\square$

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