The Stacks project

Definition 70.6.2. Let $S$ be a scheme. Let $X$ be a locally Noetherian integral algebraic space over $S$.

  1. A prime divisor is an integral closed subspace $Z \subset X$ of codimension $1$, i.e., the generic point of $|Z|$ is a point of codimension $1$ on $X$.

  2. A Weil divisor is a formal sum $D = \sum n_ Z Z$ where the sum is over prime divisors of $X$ and the collection $\{ |Z| : n_ Z \not= 0\} $ is locally finite in $|X|$ (Topology, Definition 5.28.4).

The group of all Weil divisors on $X$ is denoted $\text{Div}(X)$.

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