Definition 31.27.4. Let X be a locally Noetherian integral scheme. Let \mathcal{L} be an invertible \mathcal{O}_ X-module.
For any nonzero meromorphic section s of \mathcal{L} we define the Weil divisor associated to s as
\text{div}_\mathcal {L}(s) = \sum \text{ord}_{Z, \mathcal{L}}(s) [Z] \in \text{Div}(X)where the sum is over prime divisors.
We define Weil divisor class associated to \mathcal{L} as the image of \text{div}_\mathcal {L}(s) in \text{Cl}(X) where s is any nonzero meromorphic section of \mathcal{L} over X. This is well defined by Lemma 31.27.3.
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