Timeline for Torsors and Central Extensions
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 21, 2017 at 23:03 | vote | accept | João Dias | ||
| Jun 22, 2015 at 18:26 | answer | added | Will Sawin | timeline score: 6 | |
| Jun 22, 2015 at 17:43 | comment | added | Jason Starr | I suspect that you are asking why every $A$-torsor over $G$ arises from a central extension. This is not true, for instance, if $G$ is a projective complex torus and $A$ is $\mathbb{G}_m$: only torsors in $\text{Pic}^0$ will arise from central extensions (consider the pullback to the universal cover). For semisimple algebraic groups, I believe it is true that every $\mathbb{G}_m$-torus arises from a central extension, i.e., the Picard group of a simply connected semisimple algebraic group is trivial. I am not certain what happens for general linear algebraic groups . . . | |
| Jun 22, 2015 at 17:10 | comment | added | Jason Starr | You have the wrong definition of $G$-torsor. The definition you write is quite related to the definition of $G$-torsor, but it is different. | |
| Jun 22, 2015 at 17:01 | history | asked | João Dias | CC BY-SA 3.0 |