Timeline for Smoothness and smoothness over formal neighborhood
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 2, 2015 at 13:16 | comment | added | Laurent Moret-Bailly | @prochet: sorry, I had misread $\mathbb{A}^n$ for $\mathbb{A^N}$. And no, I don't know an example. | |
| Dec 9, 2014 at 19:16 | comment | added | prochet | Also I don't see why $\mathbb{A}^{\mathbb{N}}=Spec(k[x_{i}])_{i\in\mathbb{N}}$ is locally noetherian. | |
| Dec 9, 2014 at 19:02 | comment | added | prochet | so then, for such a $Y$, we can find an etale neighborhood as mentioned in the question? More generally, if we have a scheme $X$ and a point x, such that $X_{x}$ is isomorphic to $\mathbb{A}^{\mathbb{N}}_{y}$ can we also find such an etale neighborhood? | |
| Dec 7, 2014 at 8:36 | comment | added | Laurent Moret-Bailly | @prochet: as ACL notes, there is no such example if $Y$ is locally noetherian. | |
| Dec 6, 2014 at 22:52 | comment | added | prochet | and can we find an example if $Y=\mathbb{A}^{\mathbb{N}}$? | |
| Nov 20, 2014 at 10:48 | comment | added | Laurent Moret-Bailly | And meanwhile, I have realized that the same example was given by Anton Geraschenko in answer to this question. | |
| Nov 20, 2014 at 10:43 | comment | added | Laurent Moret-Bailly | Right. Without this assumption, taking completions (of local rings) may lead to strange things. | |
| Nov 20, 2014 at 9:31 | comment | added | ACL | Dear Laurent. This comment is just to be sure that I understand things properly. Compared to Grothendieck's criterion in (EGA IV, 17.5.3), what is missing in the statement given by prochet is the assumption that $Y$ is locally noetherian, isn't it? | |
| Nov 19, 2014 at 21:59 | vote | accept | prochet | ||
| Nov 19, 2014 at 18:32 | history | answered | Laurent Moret-Bailly | CC BY-SA 3.0 |