Definition 31.26.2. Let $X$ be a locally Noetherian integral scheme.

A

*prime divisor*is an integral closed subscheme $Z \subset X$ of codimension $1$.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 \mid n_ Z \not= 0\} $ is locally finite (Topology, Definition 5.28.4).

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

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