Timeline for Does every morphism BG-->BH come from a homomorphism G-->H?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 3, 2019 at 12:41 | comment | added | Praphulla Koushik | I will see that stacks link :) Thank you Sir. :) | |
| Jan 3, 2019 at 12:09 | comment | added | Niels | @Praphulla Koushik : I am sorry but I have no idea for another reference. To show that a pseudo-torsor is a torsor, you have to show that is has sections locally, see stacks.math.columbia.edu/tag/0497 . | |
| Jan 3, 2019 at 10:36 | comment | added | Praphulla Koushik | I am not able to understand the way it is done.. Giraud's book is not in English and I can read only English.. :) Any other reference you can suggest :) | |
| Jan 3, 2019 at 9:34 | comment | added | Niels | @Praphulla Koushik : it is very likely you can find this in Giraud's book on non-abelian-cohomology, but honestly the best is to work it out by yourself. What don't you undertstand in the last (but one) paragraph: what I am trying to do, or the way it is done ? | |
| Jan 3, 2019 at 9:07 | comment | added | Praphulla Koushik | Sorry for not being specific (I thought I was, I will give one more try)... Can you suggest some reference where $\operatorname{\mathbf{Hom}}_{gr} (G,H) \to \operatorname{\mathbf{Hom}}(BG,BH)$ is seen as a principal $H$-bundle... I am not able to understand what you said in your last paragraph... | |
| Jan 3, 2019 at 8:34 | comment | added | Niels | @Praphulla Koushik : for your first question, this is mainly a sheaf/stack theoretic statement, there are no considerations about algebraicity (or representability). I don't understand your second question, please be more specific. | |
| Jan 2, 2019 at 14:49 | comment | added | Praphulla Koushik | I did not follow anything after "This of course answers the original question completely (globally, no ; locally, yes)". Please consider explaining last but one paragraph. | |
| Jan 2, 2019 at 14:48 | comment | added | Praphulla Koushik | I did not see this kind of things before... By $H$-torsor you mean principal $H$ bundle? So, you mean $\text{Hom}_{gr}(G,H)\rightarrow \text{Hom}(BG,BH)$ is a principal $H$-bundle. What is topology/smooth structure on $\text{Hom}_{gr}(G,H),\text{Hom}_{gr}(BG,BH)$? Just like any principal $G$ bundle $P\rightarrow M$ with $P/G=M$, you have here $\text{Hom}(G,H)/H=\text{Hom}(BG,BH)$.. You want to take quotient stack $[\text{Hom}(G,H)/H]$ (I am only recently reading about Quotient stack mathoverflow.net/questions/319038/… so I dont know much)... | |
| Jan 2, 2019 at 14:39 | history | edited | Matthieu Romagny | CC BY-SA 4.0 |
added 7 characters in body
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| Jan 2, 2019 at 14:02 | history | answered | Niels | CC BY-SA 4.0 |