The Stacks project

Definition 46.5.1. A sheaf of $\mathcal{O}$-modules $\mathcal{F}$ on $(\mathit{Sch}/S)_\tau $ is adequate if there exists a $\tau $-covering $\{ \mathop{\mathrm{Spec}}(A_ i) \to S\} _{i \in I}$ such that $F_{\mathcal{F}, A_ i}$ is adequate for all $i \in I$.

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View Definition 46.5.1 as pdf