Lemma 87.20.8. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $T \subset |X|$ be a closed subset. Let $X_{/T}$ be the formal completion of $X$ along $T$.

If $X \setminus T \to X$ is quasi-compact, then $X_{/T}$ is locally adic*.

If $X$ is locally Noetherian, then $X_{/T}$ is locally Noetherian.

## Comments (2)

Comment #2029 by Brian Conrad on

Comment #2068 by Johan on