Lemma 31.23.8. Let f : X \to Y be a morphism of locally ringed spaces. Assume that pullbacks of meromorphic functions are defined for f (see Definition 31.23.4).
Let \mathcal{F} be a sheaf of \mathcal{O}_ Y-modules. There is a canonical pullback map f^* : \Gamma (Y, \mathcal{K}_ Y(\mathcal{F})) \to \Gamma (X, \mathcal{K}_ X(f^*\mathcal{F})) for meromorphic sections of \mathcal{F}.
Let \mathcal{L} be an invertible \mathcal{O}_ Y-module. A regular meromorphic section s of \mathcal{L} pulls back to a regular meromorphic section f^*s of f^*\mathcal{L}.
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