The Stacks project

Lemma 37.29.6. Let $f : X \to Y$, $s : Y \to X$ be as in Situation 37.29.1. Assume

  1. $f$ is of finite presentation and flat, and

  2. all fibres of $f$ are geometrically reduced.

Then $X^0$ is open in $X$.

Proof. This is an immediate consequence of Lemma 37.29.5. $\square$

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