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Jul 19, 2020 at 15:09 comment added Laurent Moret-Bailly With these assumptions, the answer is no: take $X=Y\amalg Z$ where $Z$ is an non-reduced closed subscheme of $Y$.
Jul 19, 2020 at 11:43 answer added Bernie timeline score: 3
Jul 19, 2020 at 8:55 history asked Hajime_Saito CC BY-SA 4.0