The Stacks project

Definition 72.5.2. Let $S$ be a scheme. Let $X$ and $Y$ be integral algebraic spaces over $S$. Let $f : X \to Y$ be locally of finite type and dominant. Assume any of the equivalent conditions (1) – (5) of Lemma 72.5.1. Let $x \in |X|$ and $y \in |Y|$ be the generic points. Then the positive integer

\[ \deg (X/Y) = [\kappa (x) : \kappa (y)] \]

is called the degree of $X$ over $Y$.

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