Non-openness of flat locus
问题内容
If $f \colon X \to Y$ is a finite surjective morphism between integral Noetherian schemes, then the set $V\subseteq Y$ of points over which $f$ is flat is open. I want to show that this fails if we drop the finiteness assumption. I can think of an example given by blowing up $\mathbb A^3$ at a suitable closed subscheme, but the resulting map is not surjective. What should I be looking for here for a counterexample?
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