Lemma 37.29.6 (055R)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 37: More on Morphisms
Section 37.29: Connected components meeting a section
Lemma 37.29.6 (cite)

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

$f$ is of finite presentation and flat, and
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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