The Stacks project

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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