Timeline for Mysterious quotes (at least for me)
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Nov 9, 2014 at 18:16 | comment | added | Max | In your first question there was two questions. 1) Morita invariance imply dependence only on derived categories? 2)Cannot different algebras have equivalent derived categories without having equivalent categories of modules | |
| Nov 9, 2014 at 6:33 | comment | added | მამუკა ჯიბლაძე | @Max Seems like 1) has been clarified. As for 2), I don't understand how dg would change anything in the context of my comments; still, my second one is flawed. Tensor structure on modules over a commutative ring does not have to do anything with Hopf structure, and a general commutative ring does not have any. The essence is, for $A$-modules $M$ and $N$, to produce an $A$-module from the $A\otimes A$-module $M\otimes N$. Hopf structure would restrict it along the diagonal $A\to A\otimes A$; while for any commutative $A$ one may extend it along $A\otimes A\to A$. | |
| Nov 8, 2014 at 19:48 | comment | added | AAK | Right, I should have said derived Morita invariance. And Orlov's remark was about the derived category of a commutative scheme. | |
| Nov 8, 2014 at 19:13 | comment | added | Max | I'm not sure I understand your remarks. 1) Here, It is about derived Morita equivalences. 2) The point is that we are considering differential graded algebras and not only algebras. | |
| Nov 8, 2014 at 18:36 | comment | added | მამუკა ჯიბლაძე | Two things. First: does Morita invariance imply dependence only on derived categories? A priori it only means dependence only on categories of modules. Cannot different algebras have equivalent derived categories without having equivalent categories of modules? Second: afaik, derived category of a general noncommutative algebra simply does not have any monoidal structure. For that you need something like Hopf algebra structure (maybe up to Morita). | |
| Nov 6, 2014 at 17:56 | vote | accept | Max | ||
| Nov 6, 2014 at 11:36 | history | edited | AAK | CC BY-SA 3.0 |
added 10 characters in body
|
| Nov 6, 2014 at 11:26 | history | edited | AAK | CC BY-SA 3.0 |
added 30 characters in body
|
| Nov 6, 2014 at 11:21 | history | answered | AAK | CC BY-SA 3.0 |