Timeline for "Descent" of analytic functions along a finite morphism
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 14, 2017 at 8:26 | comment | added | Laurent Moret-Bailly | @Sasha: the result is false for general $Y$ (I'll edit my answer later); it might be true if $Y$ is normal. | |
| Nov 13, 2017 at 21:01 | comment | added | Sasha | @Friedrich Knop: Thank you! Just to clarify for myself, the proof below by Moret-Bailly will work too for establishing the fact I wanted, right? | |
| Nov 13, 2017 at 20:59 | comment | added | Sasha | @Laurent Moret-Bailly: It is a well-known theorem that this quotient is isomorphic to an affine space. But I guess that this doesn't really matter if one knows how to work with analytic spaces well enough, your proof below will carry? | |
| Nov 13, 2017 at 14:24 | comment | added | Laurent Moret-Bailly | Concerning the group-theoretic motivation, why is $W\backslash\mathfrak{h}$ smooth? | |
| Nov 13, 2017 at 8:42 | comment | added | Friedrich Knop | For a reference to your invariant theoretic application see my answer to mathoverflow.net/questions/237666/…. | |
| Nov 12, 2017 at 18:57 | vote | accept | Sasha | ||
| Nov 12, 2017 at 18:42 | comment | added | Sándor Kovács | @Sasha: Right, it would just mash everything into a wedge. I knew it was too simple... | |
| Nov 12, 2017 at 17:43 | answer | added | Laurent Moret-Bailly | timeline score: 9 | |
| Nov 12, 2017 at 2:49 | comment | added | Sasha | @Sándor Kovács: root $\circ$ power is not identity in general, that's your mistake if I am not mistaken? | |
| Nov 11, 2017 at 17:19 | comment | added | nfdc23 | @abx: I had the same initial gut reaction, but it is unnecessary: since $f$ is a finite surjection, hence topologically a quotient map, a function on $Y$ whose composition with $f$ is continuous must itself be continuous. | |
| Nov 11, 2017 at 17:16 | comment | added | abx | You should at least assume that your function is continuous, otherwise there are obvious counter-examples. | |
| Nov 11, 2017 at 16:48 | history | asked | Sasha | CC BY-SA 3.0 |