Definition 66.10.2. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $x \in |X|$ be a point. The dimension of the local ring of $X$ at $x$ is the element $d \in \{ 0, 1, 2, \ldots , \infty \} $ satisfying the equivalent conditions of Lemma 66.10.1. In this case we will also say $x$ is a point of codimension $d$ on $X$.
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