Lemma 21.46.8 (08G3)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 21: Cohomology on Sites
Section 21.46: Tor dimension
Lemma 21.46.8 (cite)

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Lemma 21.46.8. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $a, b \in \mathbf{Z}$ . For $K$ , $L$ objects of $D(\mathcal{O})$ if $K \oplus L$ has tor amplitude in $[a, b]$ so do $K$ and $L$ .

Proof. Clear from the fact that the Tor functors are additive. $\square$

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