Timeline for Push-forward along closed immersion
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 5, 2018 at 14:27 | history | undeleted | S. Carnahan♦ | ||
| May 9, 2018 at 13:38 | history | deleted | user120812 | via Vote | |
| May 9, 2018 at 13:35 | comment | added | user120812 | For instance, if $X$ is a Noetherian $\mathbf{F}_p$ scheme that is smooth, and $Z\subset X$ a smooth closed subscheme, then $Z^{perf}$ and $X^{perf}$ should give a counterexample choosing $\mathcal{F} = \mathcal{O}_{Z^{perf}}$. Similar to your example, in a way. I think I saw this on an answer, some time ago. | |
| May 9, 2018 at 13:33 | comment | added | user120812 | Yes but a similar counterexample should work | |
| May 9, 2018 at 13:33 | comment | added | Jason Starr | I missed the hypothesis that $X$ is a coherent $\mathcal{O}_X$-module. | |
| May 9, 2018 at 13:32 | comment | added | Jason Starr | No, that is not true. Let $X$ be $\text{Spec}\ k[x_1,x_2,x_3,\dots]$ and let $Z$ be the closed subscheme associated to the ideal $\langle x_1, x_2, x_3, \dots \rangle.$ | |
| May 9, 2018 at 13:30 | history | asked | user120812 | CC BY-SA 4.0 |