Timeline for Spin structures on schemes
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2016 at 15:34 | comment | added | Bilateral | @DonuArapura: I am precisely interested in the situation on schemes, not on manifold or complex manifolds, which is well-known. | |
| Apr 13, 2016 at 15:32 | comment | added | Donu Arapura | If I remember correctly (it's been a while) the usual condition for existence is of a spin structure on a manifold is for $w_2=0$. So for a complex manifold, it would be enough to know that $c_1$ is even, or that the canoncal bundle has a square root. These are classically called theta characteristics. This is probably different from what you are after, but I thought I'd mention it. | |
| Apr 13, 2016 at 14:19 | comment | added | Denis Nardin | I think that part of the problem is that defining a Spin structure requires a nondegenerate quadratic form on your bundle. In topology you can always choose a positive definite one (they're all equivalent anyway) but over a scheme the question is much more subtle | |
| Apr 13, 2016 at 14:16 | answer | added | Ben McKay | timeline score: 4 | |
| Apr 13, 2016 at 9:35 | history | asked | Bilateral | CC BY-SA 3.0 |