Timeline for Global functions on a flat proper family
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 13, 2019 at 9:02 | comment | added | Jason Starr | Welcome new contributor. As remarked by @gdb, this is false in general. Let $\mathcal{E}$ be any flat coherent $\mathcal{O}_X$-module such that $f_*\mathcal{E}$ is not flat. Now consider the new $R$-scheme structure on $X$ that replaces the structure sheaf $\mathcal{O}_X$ by the sheaf of $\mathcal{O}_X$-modules, $\mathcal{O}_X\oplus \left( \mathcal{E}\cdot \epsilon \right),$ with the unique structure of $\mathcal{O}_X$-algebra such that the "placeholder" $\epsilon$ satisfies $\epsilon\cdot \epsilon = 0$. | |
| Mar 13, 2019 at 1:35 | comment | added | gdb | Two remarks: it is not possible if you assume that $R$ is normal (and noetherian) or if you assume that all fibres are geom. reduced (and $R$ is noetherian). It should be false in general, but I don't know an example on the top of my head. | |
| Mar 12, 2019 at 21:33 | history | edited | YCor |
edited tags
|
|
| Mar 12, 2019 at 20:55 | review | First posts | |||
| Mar 12, 2019 at 21:01 | |||||
| Mar 12, 2019 at 20:52 | history | asked | rori | CC BY-SA 4.0 |