Definition 29.51.8. Let $X$ and $Y$ be integral schemes. Let $f : X \to Y$ be locally of finite type and dominant. Assume $[R(X) : R(Y)] < \infty$, or any other of the equivalent conditions (1) – (4) of Lemma 29.51.7. Then the positive integer

$\deg (X/Y) = [R(X) : R(Y)]$

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

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