Theorem 41.6.2. Let $Y$ be a connected scheme. Let $f : X \to Y$ be unramified and separated. Every section of $f$ is an isomorphism onto a connected component. There exists a bijective correspondence

$\text{sections of }f \leftrightarrow \left\{ \begin{matrix} \text{connected components }X'\text{ of }X\text{ such that} \\ \text{the induced map }X' \to Y\text{ is an isomorphism} \end{matrix} \right\}$

In particular, given $x \in X$ there is at most one section passing through $x$.

Proof. Direct from Proposition 41.6.1 part (3). $\square$

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