The Stacks project

Remark 64.12.3. A variant of this lemma is to consider a Noetherian scheme $X$ and the category $D_{perf}(\mathcal{O}_ X)$ of complexes which are locally quasi-isomorphic to a finite complex of finite locally free $\mathcal{O}_ X$-modules. Objects $K$ of $D_{perf}(\mathcal{O}_ X)$ can be characterized by having coherent cohomology sheaves and bounded tor dimension.

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View Remark 64.12.3 as pdf