Definition 41.21.1. Let X be a locally Noetherian scheme. A strict normal crossings divisor on X is an effective Cartier divisor D \subset X such that for every p \in D the local ring \mathcal{O}_{X, p} is regular and there exists a regular system of parameters x_1, \ldots , x_ d \in \mathfrak m_ p and 1 \leq r \leq d such that D is cut out by x_1 \ldots x_ r in \mathcal{O}_{X, p}.
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