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Not = but surjective
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aisejohan committed May 16, 2024
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Expand Up @@ -5925,7 +5925,7 @@ \section{Flat morphisms}
Then the composition $U_i \to V_i \times_Y X \to V_i$ is a surjective,
flat morphism of affines.
Of course then $U = \coprod U_i \to X$ is surjective and \'etale
and $U = V \times_Y X$. Moreover, the morphism $U \to V$ is the
and $U \to V \times_Y X$ is surjective. Moreover, the morphism $U \to V$ is the
disjoint union of the morphisms $U_i \to V_i$. Hence $U \to V$ is surjective,
quasi-compact and flat. Consider the diagram
$$
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