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 $x$.
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