The Stacks project

Remark 59.77.2. Objects in the derived category $D_{ctf}(X_{\acute{e}tale}, \Lambda )$ in some sense have better global properties than the perfect objects in $D(\mathcal{O}_ X)$. Namely, it can happen that a complex of $\mathcal{O}_ X$-modules is locally quasi-isomorphic to a finite complex of finite locally free $\mathcal{O}_ X$-modules, without being globally quasi-isomorphic to a bounded complex of locally free $\mathcal{O}_ X$-modules. The following lemma shows this does not happen for $D_{ctf}$ on a Noetherian scheme.