Lemma 21.44.10. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $E$ be an object of $D(\mathcal{O})$. Let $a, b \in \mathbf{Z}$.

If $E$ has tor amplitude in $[a, b]$, then for every point $p$ of the site $\mathcal{C}$ the object $E_ p$ of $D(\mathcal{O}_ p)$ has tor amplitude in $[a, b]$.

If $\mathcal{C}$ has enough points, then the converse is true.

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