Timeline for About the inverse function theorem in the étale topology
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 4, 2022 at 8:45 | comment | added | Adrien MORIN | Have you had a look at math.stackexchange.com/questions/3314133/… ? | |
| Jan 19, 2022 at 17:46 | comment | added | Piotr Achinger | This is meant to be a tautology. If $df_p$ is an isomorphism, i.e. $f$ is etale at $p$, then there exists an open neighborhood $V$ of $p$ such that $f|_V$ is etale. This $V$ is then an etale neighborhood of $f(p)$, and so $f$ tautologically gives an isomorphism from $V$ (a neighborhood of $p$) to $V$ (a neighborhood of $f(p)$). | |
| Jan 19, 2022 at 17:40 | comment | added | Gabriel | @DenisNardin Could you give more details about why this is trivial if we replace the source as well? I get that (1) is used for proving that $f$ is étale, but I don't see how to find the étale neighborhood of $p$. | |
| Jan 19, 2022 at 17:32 | comment | added | Denis Nardin | The last statement you ask about is false even in the differentiable category (just take any non-trivial covering space). If you allow the source to be replaced by an étale neighborhood of $p$ as well, this makes the statement true and a trivial consequence of your property (1). | |
| Jan 19, 2022 at 17:29 | history | asked | Gabriel | CC BY-SA 4.0 |