Timeline for Principal bundles in the etale and Zariski topology and extensions of the structure group
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 3, 2011 at 20:59 | comment | added | Jason Starr | If you say so. I do know something about non-Abelian cohomology. I certainly understand Angelo's answer. I do not see how what you wrote is "essentially" what he wrote. | |
| Aug 3, 2011 at 12:58 | comment | added | anon | @Jason, sorry, I don't understand your question. The argument Angelo gives is essentially that in my comment, but with the cohomology removed. | |
| Aug 3, 2011 at 5:10 | vote | accept | solbap | ||
| Aug 3, 2011 at 3:54 | answer | added | Angelo | timeline score: 5 | |
| Aug 3, 2011 at 1:48 | comment | added | Jason Starr | Dear solbap -- There is a long exact sequence, of sorts, for a central extension of a group $G''$ by a group $G'$, cf. Section I.5.7 of Serre's "Galois Cohmology". This is stated only in the case that $X$ is the spectrum of a field (so that \'etale cohomology is Galois cohomology). The generalization to schemes may be contained in Giraud's thesis. | |
| Aug 3, 2011 at 1:44 | comment | added | Jason Starr | Dear anon -- What? | |
| Aug 2, 2011 at 23:51 | comment | added | anon | Let $f\colon X_{et}\to X_{zar}$ be the identity map. For a special group $G$, $R^1f_*G=0$ and so the Leray spectral sequence shows that the map from $H^2_{zar}$ to $H^2_{et}$ is injective in the commutative case, which is what you want in order to apply the 5-lemma. It is surely also true in the noncommutative case, but writing down a proof will be more complicated. | |
| Aug 2, 2011 at 23:05 | history | asked | solbap | CC BY-SA 3.0 |