Timeline for Examples of injective morphisms which are not universally injective
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 25, 2012 at 22:13 | comment | added | Jérémy Blanc | Yes. This is probably too specialised for EGA, even if it corresponds, for me, to the "geometric" case. | |
| Nov 25, 2012 at 21:29 | vote | accept | Jérémy Blanc | ||
| Nov 25, 2012 at 19:17 | comment | added | Damian Rössler | Notice that Angelo's proof below uses the fact that the schemes are locally of finite type over a field. EGA makes no assumption on the schemes. | |
| Nov 25, 2012 at 16:19 | comment | added | Jérémy Blanc | Thanks! Sorry for my ignorance about characteristic $p$. I still don't get why EGA talks about all alg. closed fields if only one is enough. In Altman/Kleiman "Introduction to Grothendieck Duality Theory" Prop. 5.2, they also make many equivalence definitions of radicial and always include to check all fields. Seems weird not to say that one can only check on one algebraically closed field. | |
| Nov 25, 2012 at 16:12 | comment | added | Damian Rössler | (answer to your comment below) $x\to x^p$ is not étale: it would then be smooth and then its differential would be non vanishing but in fact $d(x^p)=p\cdot x^{p-1}dx=0$ because $p=0$. Apart from that, you are right about EGA: it talks about every alg. closed field, not just one so it is weaker than Angelo's statement. I removed my comment. | |
| Nov 25, 2012 at 10:02 | answer | added | Angelo | timeline score: 12 | |
| Nov 25, 2012 at 8:28 | history | asked | Jérémy Blanc | CC BY-SA 3.0 |