Timeline for How to make commutative algebraic groups strongly dualizable?
Current License: CC BY-SA 2.5
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 4, 2009 at 16:12 | vote | accept | Ilya Nikokoshev | ||
| Nov 4, 2009 at 16:12 | vote | accept | Ilya Nikokoshev | ||
| Nov 4, 2009 at 16:12 | |||||
| Nov 3, 2009 at 22:26 | answer | added | Greg Stevenson | timeline score: 1 | |
| Nov 3, 2009 at 16:08 | comment | added | S. Carnahan♦ | There is a (stable infinity) category of complexes of abelian sheaves on a base, but not all objects are strongly dualizable. You need some kind of finiteness to get good duality. | |
| Nov 3, 2009 at 15:12 | comment | added | Ilya Nikokoshev | I think the last part of what you say should be close to what I'm looking for, thanks for writing it! Is there some category of "derived abelian groups" where all elements are strongly dualizable? Do you mind writing it in the answer area so that I can upvote you? | |
| Nov 3, 2009 at 15:08 | history | edited | Ilya Nikokoshev | CC BY-SA 2.5 |
final, hopefully, edit
|
| Nov 3, 2009 at 10:22 | comment | added | Greg Stevenson | I wasn't trying to point out that anything in particular was a rigid tensor category - I wasn't sure exactly which category we were in. I just wanted to remark (in a way that was somewhat unclear I guess) that you were basically asking for an object to be strongly dualizable. Also (although this is not completely related) one can sometimes make perfectly reasonable sense of Hom(A,B) = A^* \otimes B. For instance if A and B are f.g. abelian groups, Hom is RHom and \otimes is \otimes^L. | |
| Nov 3, 2009 at 9:41 | comment | added | S. Carnahan♦ | This is better. | |
| Nov 3, 2009 at 8:50 | history | edited | Ilya Nikokoshev | CC BY-SA 2.5 |
fixes
|
| Nov 3, 2009 at 8:21 | history | edited | Ilya Nikokoshev | CC BY-SA 2.5 |
clarified
|
| Nov 3, 2009 at 8:12 | history | edited | Ilya Nikokoshev | CC BY-SA 2.5 |
clarified
|
| Nov 3, 2009 at 3:40 | answer | added | S. Carnahan♦ | timeline score: 1 | |
| Nov 3, 2009 at 2:59 | comment | added | S. Carnahan♦ | -1. Please make your questions more specific. In particular, you haven't mentioned a category in which B lives. | |
| Nov 2, 2009 at 22:44 | comment | added | Qiaochu Yuan | I'm afraid I don't follow. What does Hom(Hom(A, B), B) mean if A, B aren't commutative? | |
| Nov 2, 2009 at 20:25 | history | edited | Ilya Nikokoshev | CC BY-SA 2.5 |
fixes
|
| Nov 2, 2009 at 20:24 | comment | added | Ilya Nikokoshev | Indeed, "could be true for (some) B" = "could you give an example of B such that (*) holds for all A". Rigid tensor vategory -- sure, but I don't think groups form a rigid tensor category! | |
| Nov 2, 2009 at 20:15 | comment | added | Greg Stevenson | I am a bit confused about the question - you want other algebraic groups for which (*) holds? Or other situations more generally? With regards to your last statement one can write such things in any rigid tensor category. | |
| Nov 2, 2009 at 20:03 | history | asked | Ilya Nikokoshev | CC BY-SA 2.5 |