I am trying to prove that, given a proper morphism of schemes $f \colon X \rightarrow Y$, if $Y$ and all fibers of $f$ are connected then $X$ is connected. It seems to me that it would help knowing if $f$ is surjective, so I am wondering if it follows from these hypotheses.
2026-04-12 19:43:26.1776023006
Surjectivity of proper morphism
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