Lemma 71.10.10. Let S be a scheme. Let f : X \to Y be a morphism of algebraic spaces over S. Assume that pullbacks of meromorphic functions are defined for f (see Definition 71.10.6).
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}_ X-module. A regular meromorphic section s of \mathcal{L} pulls back to a regular meromorphic section f^*s of f^*\mathcal{L}.
Comments (0)