Definition 87.38.1 (0GXU)—The Stacks project

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Table of contents
Part 5: Topics in Geometry
Chapter 87: Formal Algebraic Spaces
Section 87.38: Completion along a closed subspace
Definition 87.38.1 (cite)

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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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