Timeline for Derived equivalent varieties with differing integral Mukai-Hodge structures?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 13, 2015 at 16:09 | comment | added | Mikhail Bondarko | Probablly you are right. Yet it seems that noncommutative motives may give an answer. | |
| Dec 13, 2015 at 15:23 | comment | added | AAK | @MikhailBondarko, it's not quite so easy, I'm afraid. You would need to be able to define Betti cohomology and Hodge structures at the level of dg-categories, something which is most likely impossible in my opinion. The best you have are noncommutative Hodge structures on Hochschild homology and variants, studied by Kaledin and others. | |
| Dec 12, 2015 at 16:02 | comment | added | Mikhail Bondarko | The non-commutative motive functor does satisfy certain universality property (actuallya, there are several functors with distinct universality properties;)): in theory, this should describe which functors factor through this one. | |
| Dec 12, 2015 at 14:52 | comment | added | Dominik | @MikhailBondarko: By "positive answer", do you mean that there are no such counterexamples? I'm a bit familiar with Tabuada's theory; could you expand on your comment? | |
| Dec 12, 2015 at 13:24 | history | edited | Mikhail Bondarko |
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| Dec 12, 2015 at 13:11 | comment | added | Mikhail Bondarko | Probably, the theory of non-commutative motives (as developed by Gonsalo Tabuada and his numerous co-authors) yields a positive answer to your question. | |
| Dec 10, 2015 at 15:50 | history | asked | Dominik | CC BY-SA 3.0 |