Timeline for Is every homogeneous G-variety of the form G/H?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 25, 2010 at 15:51 | answer | added | inkspot | timeline score: 3 | |
| Apr 3, 2010 at 13:29 | vote | accept | user717 | ||
| Apr 2, 2010 at 12:44 | comment | added | José Figueroa-O'Farrill | @Joel: your suggested edit has been done. | |
| Apr 2, 2010 at 12:43 | history | edited | José Figueroa-O'Farrill | CC BY-SA 2.5 |
edited title
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| Apr 2, 2010 at 12:38 | comment | added | BCnrd | Must assume $G$ and $X$ are smooth (or reduced; leads to the same since $k$ alg closed). Otherwise can have things like $G$ infinitesimal and $X = {\rm{Spec}}(k)$. Role of smoothness in proof is that for $x \in X(k)$, orbit map $G \rightarrow X$ is a surjective with all fibers equidimensional of the same dim., necessarily the "right" value (difference of pure dim's of $G$ and $X$), and so smoothness allow to apply "miracle flatness theorem" (23.1, Matsumura CRT) to deduce orbit map is (faithfully) flat. Thus, $G/G_x \rightarrow X$ is isom due to faithfully flat descent theory. | |
| Apr 2, 2010 at 12:27 | comment | added | Joel Fine | For those of us in pedants' corner, could someone edit the title to read "Is every homogeneous G-variety of the form G/H"? Thank you. | |
| Apr 2, 2010 at 10:13 | answer | added | Torsten Ekedahl | timeline score: 16 | |
| Apr 2, 2010 at 9:43 | history | asked | user717 | CC BY-SA 2.5 |