Timeline for (corrected) When does a torsor trivialize over the algebraic closure?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 16, 2014 at 19:23 | vote | accept | Wanderer | ||
| Sep 5, 2011 at 6:07 | history | edited | Wanderer | CC BY-SA 3.0 |
edited title
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| Sep 4, 2011 at 23:25 | comment | added | Wanderer | OK, I see why the question was confusing. This should be better. | |
| Sep 4, 2011 at 23:24 | history | edited | Wanderer | CC BY-SA 3.0 |
corrected question
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| Aug 30, 2011 at 17:53 | comment | added | Jason Starr | @Moret-Bailly: That was also the counterexample I had in mind. | |
| Aug 30, 2011 at 16:22 | answer | added | Taylor Dupuy | timeline score: 1 | |
| Aug 30, 2011 at 7:18 | comment | added | Laurent Moret-Bailly | Take $k$ algebraically closed, $S=\mathbb{G}_{m,k}$, $G=\mu_2$, and $X=S\to S$ the squaring map. | |
| Aug 30, 2011 at 6:04 | comment | added | Wanderer | @Emerton: might be (not sure) but anyway, $\text{Pic}\ \overline{S} = 0$ implies $\text{Pic}^0\ \overline{S} = 0$... @S. Carnahan: yes :) @Jason Starr: you can impose this as en extra condition, however in the specific situation I'm looking at $S$ will not be proper (there $S$ will be the affine line with some points removed and $G$ will be a torus). | |
| Aug 30, 2011 at 2:44 | comment | added | Emerton | Maybe you mean $Pic^0 \overline{S}$, rather than $Pic \overline{S}$, in your final sentence? | |
| Aug 30, 2011 at 0:20 | comment | added | S. Carnahan♦ | Minor nitpick: you probably want the isomorphism $\bar{X} \to \bar{G}$ to be $\bar{G}$-equivariant. | |
| Aug 29, 2011 at 23:58 | comment | added | Jason Starr | Is $S$ proper over $k$? Otherwise there are counterexamples where $S$ equals the multiplicative group scheme $\mathbb{G}_{m,k}$. | |
| Aug 29, 2011 at 23:25 | history | edited | Wanderer | CC BY-SA 3.0 |
edited title
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| Aug 29, 2011 at 22:59 | comment | added | Michael Thaddeus | How is the right-hand side different from $\overline{G}$? | |
| Aug 29, 2011 at 22:49 | history | asked | Wanderer | CC BY-SA 3.0 |