Lemma 86.21.3. Let $S$, $f : X' \to X$, $T \subset |X|$, $U \subset X$, $T' \subset |X'|$, and $U' \subset X'$ be as in Section 86.20. If $X$ is locally Noetherian, $f$ is proper, and $U' \to U$ is an isomorphism, then $f_{/T} : X'_{/T'} \to X_{/T}$ is a formal modification.

Proof. By Formal Spaces, Lemmas 85.16.6 the source and target of the arrow are locally Noetherian formal algebraic spaces. The other conditions follow from Lemmas 86.20.3, 86.20.8, 86.20.9, and 86.20.10. $\square$

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