Timeline for The relation between t-structures and derived category
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| May 19, 2020 at 15:07 | vote | accept | Amos Kaminski | ||
| May 19, 2020 at 15:07 | |||||
| May 19, 2020 at 14:18 | comment | added | Simone Virili | Of course, you need sequential homotopy co/limits to exist, and that they are computed "pointwise" in a suitable sense. If the t-structure is taken on the base of a strong and stable derivator (e.g., the homotopy category of a bicomplete stable $\infty$-category), then all such requirements are satisfied. An alternative to derivators is probably to develop a theory of f-categories (like Beilinson did for bounded Z-filtrations) for these "tridimensional" filtrations, but I have not tried to do so. | |
| May 19, 2020 at 14:13 | comment | added | Simone Virili | I had tried some time ago to just consider unbounded filtrations and I could not make things work. There is another option, that I developed in a recent preprint: consider "tridimensional filtrations", that is, objects filtered by ZxNxN^{op}, where the Z-filtration is "point-wise bounded". The Beilinson-Bernstein-Deligne-Gabber realization then allows you to see such objects as "NxN^{op}"-shaped diagrams of bounded objects, and then you can take a sequential homotopy colimit in the N-direction, and a sequential homotopy limit in the N^{op}-direction. | |
| May 19, 2020 at 12:27 | history | answered | Dan Petersen | CC BY-SA 4.0 |