Timeline for Does derived algebraic geometry allow us to take quotients with reckless abandon?
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| Feb 7, 2011 at 12:38 | vote | accept | Harry Gindi | ||
| Feb 7, 2011 at 3:57 | comment | added | David Roberts♦ | I know you are familiar with homotopy quotients, but I was more wondering whether the rationale behind the condition for a stack quotient implies there are any conditions necessary for homotopy quotients. Quite possibly my concerns are misplaced, and one doesn't care about local representability by a simplicial scheme, or what-have-you, but it would be interesting to see what happens in practice. | |
| Feb 7, 2011 at 3:43 | comment | added | Harry Gindi | @Scott: Yes, I'm familiar with the details. I meant what I said in a very nuanced way that I didn't feel was worth elaborating on. | |
| Feb 7, 2011 at 3:39 | comment | added | S. Carnahan♦ | @Harry: You can't take a homotopy quotient of objects in the homotopy category. You need a diagram in the "honest" category. | |
| Feb 7, 2011 at 3:35 | answer | added | S. Carnahan♦ | timeline score: 13 | |
| Feb 7, 2011 at 3:14 | comment | added | Harry Gindi | Yes, I realize that they should be homotopy quotients. That was implied. Taking strict quotients of derived stacks wouldn't make sense, since they're objects of the homotopy category. | |
| Feb 7, 2011 at 3:10 | comment | added | David Roberts♦ | Your guess about alg. spaces and stacks is pretty much on the money. But you are not just taking quotients when doing DAG, but homotopy colimits. The requirement that the groupoid action is smooth when describing an algebraic stack is necessary to make sure the resulting stack has a cover by a map in an appropriate pretopology. It may be that when considering quotients by arbitrary actions you are really 'doing' in homotopy quotients. I'm not sure though if one needs to worry about local representability by simplicial objects for derived stacks or something. | |
| Feb 7, 2011 at 2:52 | history | edited | Harry Gindi | CC BY-SA 2.5 |
added 28 characters in body
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| Feb 7, 2011 at 1:48 | history | asked | Harry Gindi | CC BY-SA 2.5 |