Skip to main content
8 events
when toggle format what by license comment
Jun 30, 2012 at 16:20 vote accept AFK
May 4, 2011 at 22:14 vote accept AFK
May 4, 2011 at 22:14
May 14, 2010 at 15:47 comment added Torsten Ekedahl @David: Yes, the non-split case is a problem for the relative Tannakian which will no doubt result in me actually reading through your answer :-)
May 14, 2010 at 13:32 comment added David Ben-Zvi Torsten - thanks, that is more Tannakian! (I guess the description I gave should extend to nonsplit group extensions, but in the split case may be overkill)
May 14, 2010 at 4:18 comment added Torsten Ekedahl ... In this case the group scheme is just $K$ with the given action of $H$ (of course it may not be a finite group scheme so its affine algebra may not lie in $Rep_k(H)$ but rather in the category of ind-objects for $Rep_k(H)$.
May 14, 2010 at 4:18 comment added Torsten Ekedahl A more Tannakian answer along the same lines is relative Tannakian theory. Restriction to $H$ gives a fibre functor $Rep_k(G) \to Rep_k(H)$ and the surjection $G\to H$ gives a "constant object" functor $Rep_k(H) \to Rep_k(G)$. One can imitate the usual Tannaka theory replacing $Rep_k(1)=Vec_k$ by $Rep_k(H)$ getting a description of $Rep_k(G)$ as the category of modules in $Rep_k(H)$ of some group scheme in $Rep_k(H)$. ....
May 13, 2010 at 23:45 history edited David Ben-Zvi CC BY-SA 2.5
added 60 characters in body
May 13, 2010 at 23:19 history answered David Ben-Zvi CC BY-SA 2.5