Timeline for Stable curves over non-noetherian schemes
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 7, 2023 at 14:37 | comment | added | Alexander Betts | I concur with your comments -- it does seem like the words "finitely presented" should be included in the definition, even if perhaps they are implied (very non-obviously!) by the other conditions. Thanks for the comments, this has really cleared this up for me! | |
| Dec 6, 2023 at 15:23 | comment | added | Laurent Moret-Bailly | @gdb: Thanks for this link! De Jong's "wild guess" is very intriguing. And I had overlooked the fact that the genus is assumed constant. Of course I agree with the last paragraph in the blog: the right definition should include finite presentation even if the wild guess is correct. | |
| Dec 6, 2023 at 15:00 | comment | added | gdb | math.columbia.edu/~dejong/wordpress/?p=1117 | |
| Dec 5, 2023 at 17:41 | comment | added | Laurent Moret-Bailly | You said it all: the definition in D-M is not the right one, and is not the definition they use, e.g. for the complete intersection property you pointed out. In fact, Proposition (5.1) ($\mathscr{M}_g$ is separated of finite type over $\mathbb{Z}$) implies that stable curves are finitely presented! For your specific question, you get easy counterexamples from the Stack Project examples you mention. | |
| Dec 5, 2023 at 13:44 | history | asked | Alexander Betts | CC BY-SA 4.0 |