Timeline for admissible subcategories over non algebraically closed fields
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| May 29, 2013 at 11:53 | vote | accept | IMeasy | ||
| May 29, 2013 at 8:52 | answer | added | Sasha | timeline score: 2 | |
| May 28, 2013 at 16:35 | comment | added | Fernando Muro | @IMeasy, I'm not really familiar with your particular context, but I have the experience that many reasonable things like this happen at the level of models but not at the level of derived categories. Put it this other way, if it happens at the level of derived categories, it is not categorical nonsense but a kind of a result. | |
| May 28, 2013 at 13:51 | comment | added | IMeasy | good point, thank you. Still, in smaller generality one can use the results of arxiv.org/abs/0711.1734. SInce the embedding in $D^b(\bar{X})$ is given by the base change of the FM kernel, it should preserve admissibility, no? | |
| May 28, 2013 at 11:21 | comment | added | Fernando Muro | @IMeasy, beware that $D^b(\bar X)$ is not any scalar extension of $D^b(X)$. If you take a triangulated category $T$ defined over a field $k$ (i.e. hom sets are $k$-vector spaces) then $T\otime_k\bar k$ is just a $\bar k$-linear additive category, it doesn't carry any induced triangulated structure. | |
| May 28, 2013 at 11:08 | comment | added | IMeasy | It is the subcategory of $D^b(\bar{X})$ obtained as a scalar extension of $A$. | |
| May 28, 2013 at 9:08 | comment | added | Fernando Muro | What's $\bar A$? | |
| May 28, 2013 at 6:19 | comment | added | IMeasy | Yes, in fact I edited the question a little bit in order to make it clearer what I meant. Thank you. | |
| May 28, 2013 at 6:18 | history | edited | IMeasy | CC BY-SA 3.0 |
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| May 27, 2013 at 20:25 | comment | added | Fernando Muro | Notice that your definition of admissible doesn't depend on a ground field. | |
| May 27, 2013 at 20:18 | history | asked | IMeasy | CC BY-SA 3.0 |