Lemma 20.49.8 (09J5)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 20: Cohomology of Sheaves
Section 20.49: Perfect complexes
Lemma 20.49.8 (cite)

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Lemma 20.49.8. Let $(X, \mathcal{O}_ X)$ be a ringed space. If $K, L$ are perfect objects of $D(\mathcal{O}_ X)$ , then so is $K \otimes _{\mathcal{O}_ X}^\mathbf {L} L$ .

Proof. Follows from Lemmas 20.49.5, 20.47.5, and 20.48.7. $\square$

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