Timeline for Relative generic flatness.
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 10, 2012 at 8:39 | comment | added | Laurent Moret-Bailly | That's right. The "open" bit is also stated at the end of (11.3.10). | |
| Feb 10, 2012 at 2:45 | comment | added | Rami | I think I got it. EGA IV (11.3.10) says that $\\{x\in X| f|_{h ^{-1}(h(x))} : h ^{-1}(h(x)) \to g ^{-1}(h(x)) \text{ is flat at } x \\} = \\{ x \in X| f \text{ is flat at } x \\}$. and EGA IV (11.3.1) says that the later is open. Please correct me if I'm wrong. Thank you very much. | |
| Feb 9, 2012 at 23:02 | vote | accept | Rami | ||
| Feb 9, 2012 at 21:34 | comment | added | Rami | I know that a map $f:X \to Y$ is flat in an open subset $U \subset X$. I just do not undestand why it implies what I need. Do you claim that $\\{x\in X| f|_{h ^{-1}(h(x))} : h ^{-1}(h(x)) \to g ^{-1}(h(x)) \text{ is flat at } x \\} =$ $ = \\{ x \in X| f \text{ is flat at } x \\} $ ? Why? | |
| Feb 9, 2012 at 16:41 | history | answered | Laurent Moret-Bailly | CC BY-SA 3.0 |