Timeline for Bounded derived categories of which smooth projectives possess bounded t-structures whose hearts are categories of modules?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 25, 2021 at 21:05 | comment | added | Evgeny Shinder | A good reference is Orlov's paper on smooth and proper triangulated dg-categories: arxiv.org/abs/1402.7364 | |
| Nov 25, 2021 at 8:36 | comment | added | Mikhail Bondarko | Well, not all t-structures come from isomorphisms to the corresponding derived category. However, examples of tilting objects are certainly interesting to me. And may I ask you to explain "this corresponds to P being smooth proper"? I can prove something like that; yet possibly you know more nice statements on this matter. | |
| Nov 24, 2021 at 20:08 | comment | added | Evgeny Shinder | Regarding exceptional collections, it not true that if $R$ is a finite dimensional $k$-algebra of finite global dimension (this corresponds to $P$ being smooth proper) has a full exceptional collection in $D^b(R-mod)$. | |
| Nov 24, 2021 at 20:06 | comment | added | Evgeny Shinder | I think what you ask for is existing of a tilting generator $T$ in $D^b(P)$; then $R = End(T)$ is the corresponding ring, in fact, finite-dimensional noncommutative $k$-algebra. | |
| Nov 24, 2021 at 6:31 | history | edited | Mikhail Bondarko | CC BY-SA 4.0 |
added 176 characters in body
|
| Nov 24, 2021 at 5:47 | history | asked | Mikhail Bondarko | CC BY-SA 4.0 |