Lemma 32.20.2. Let $S$ be a scheme. Let $s \in S$ be a closed point such that $U = S \setminus \{ s\} \to S$ is quasi-compact. With $V = \mathop{\mathrm{Spec}}(\mathcal{O}_{S, s}) \setminus \{ s\} $ there is an equivalence of categories

where on the right hand side we consider triples consisting of a $\mathcal{O}_ U$-module $\mathcal{G}$ of finite presentation, a $\mathcal{O}_{\mathop{\mathrm{Spec}}(\mathcal{O}_{S, s})}$-module $\mathcal{H}$ of finite presentation, and an isomorphism $\alpha : \mathcal{G}|_ V \to \mathcal{H}|_ V$ of $\mathcal{O}_ V$-modules.

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