The Stacks project

Situation 97.27.1. Let $S$ be a locally Noetherian scheme. Let $X'$ be an algebraic space locally of finite type over $S$. Let $T' \subset |X'|$ be a closed subset. Let $U' \subset X'$ be the open subspace with $|U'| = |X'| \setminus T'$. Let $W$ be a locally Noetherian formal algebraic space over $S$ with $W_{red}$ locally of finite type over $S$. Finally, we let

\[ g : X'_{/T'} \longrightarrow W \]

be a formal modification, see Algebraization of Formal Spaces, Definition 87.24.1. Recall that $X'_{/T'}$ denotes the formal completion of $X'$ along $T'$, see Formal Spaces, Section 86.14.

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