The Stacks project

Lemma 72.5.3. Let $S$ be a scheme. Let $X$, $Y$, $Z$ be integral algebraic spaces over $S$. Let $f : X \to Y$ and $g : Y \to Z$ be dominant morphisms locally of finite type. Assume any of the equivalent conditions (1) – (5) of Lemma 72.5.1 hold for $f$ and $g$. Then

\[ \deg (X/Z) = \deg (X/Y) \deg (Y/Z). \]

Proof. This comes from the multiplicativity of degrees in towers of finite extensions of fields, see Fields, Lemma 9.7.7. $\square$

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