Lemma 53.2.1. Let k be a field. Let X be a curve and Y a proper variety. Let U \subset X be a nonempty open and let f : U \to Y be a morphism. If x \in X is a closed point such that \mathcal{O}_{X, x} is a discrete valuation ring, then there exist an open U \subset U' \subset X containing x and a morphism of varieties f' : U' \to Y extending f.
Proof. This is a special case of Morphisms, Lemma 29.42.5. \square
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