Remark 42.29.7. Let f : X' \to X be a morphism of schemes locally of finite type over S as in Situation 42.7.1. Let (\mathcal{L}, s, i : D \to X) be a triple as in Definition 42.29.1. Then we can set \mathcal{L}' = f^*\mathcal{L}, s' = f^*s, and D' = X' \times _ X D = Z(s'). This gives a commutative diagram
\xymatrix{ D' \ar[d]_ g \ar[r]_{i'} & X' \ar[d]^ f \\ D \ar[r]^ i & X }
and we can ask for various compatibilities between i^* and (i')^*.
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