Timeline for do geometric fibers determine scheme-theoretic image?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 30, 2011 at 10:57 | vote | accept | IMeasy | ||
| Aug 30, 2011 at 7:27 | comment | added | Laurent Moret-Bailly | @Anton: yes, that's also how I see it. | |
| Aug 30, 2011 at 6:34 | comment | added | Anton Geraschenko | Wonderful argument! The confusing part for me is why proper bijective implies finite birational in characteristic zero. I see that proper and quasi-finite implies finite. Because of characteristic zero, we have that the map is smooth on an open upstairs (right?), so it is smooth on an open set of the base (finite bijection implies homeomorphism?). Now there is an open set in the base where the map is finite, smooth (so etale), with connected fibers, so is an isomorphism. Is this the right approach? | |
| Aug 29, 2011 at 18:36 | history | answered | Laurent Moret-Bailly | CC BY-SA 3.0 |