The Stacks project

Definition 87.38.1. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $Z \subset X$ be a closed subspace and denote $Z_ n \subset X$ the $n$th order infinitesimal neighbourhood. The formal algebraic space

\[ X^\wedge _ Z = \mathop{\mathrm{colim}}\nolimits Z_ n \]

(see Lemma 87.36.2) is called the completion of $X$ along $Z$.

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View Definition 87.38.1 as pdf