Timeline for Multiple of a flat family of subschemes is flat
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 8, 2018 at 8:38 | vote | accept | Raffaele C | ||
| Oct 6, 2018 at 10:51 | answer | added | Jason Starr | timeline score: 5 | |
| Oct 5, 2018 at 12:22 | comment | added | Jason Starr | No, that is not true. Let $X$ be $\text{Spec}\ k[x,y]/\langle xy \rangle.$ Let $S$ be $\text{Spec}\ k[\epsilon]/\langle \epsilon^2 \rangle.$ Let $I$ be $\langle x,y-\epsilon\rangle.$ Then $\mathcal{O}_{X\times S}/\mathcal{I}^2$ is a direct sum of two copies of $\mathcal{O}_S$ (generated by $1$ and $y$) plus one summand $\mathcal{O}_S/\epsilon \mathcal{O}_S$ (generated by $x$). It is not $\mathcal{O}_S$-flat. | |
| Oct 5, 2018 at 12:05 | history | edited | Raffaele C | CC BY-SA 4.0 |
more precise setting
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| Oct 5, 2018 at 10:43 | history | asked | Raffaele C | CC BY-SA 4.0 |