The Stacks project

[Expose X, Proposition 1.2, p. 262, SGA1].

Lemma 58.15.1. Let $f : X \to S$ be a proper morphism of schemes. Let $X \to S' \to S$ be the Stein factorization of $f$, see More on Morphisms, Theorem 37.53.5. If $f$ is of finite presentation, flat, with geometrically reduced fibres, then $S' \to S$ is finite ├ętale.

Proof. This follows from Derived Categories of Schemes, Lemma 36.32.8 and the information contained in More on Morphisms, Theorem 37.53.5. $\square$


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