Timeline for Reconstruct a variety from its crystalline topos
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 1, 2020 at 23:49 | comment | added | Matthias Hutzler | Thanks, @ZhenLin, I now agree with your first comment. Ironically, an argument similar to the one in my answer works for the étale case (I think) but not for the crystalline case. | |
| Oct 1, 2020 at 23:43 | history | edited | Matthias Hutzler | CC BY-SA 4.0 |
indicated an error
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| Oct 1, 2020 at 22:46 | comment | added | Zhen Lin | @MatthiasHutzler The question there is different, by my understanding. It asks for a reconstruction of $(X, O_X)$, or at least some cohomological invariants, from the petit étale topos as an abstract topos (so, without the structure sheaf). | |
| Oct 1, 2020 at 22:36 | comment | added | Matthias Hutzler | @ZhenLin The answer to this other question implies that it doesn't work in the ètale case. | |
| Oct 1, 2020 at 22:34 | comment | added | Matthias Hutzler | @JoeT Thinking about your comment made me realize that my above argument is probably wrong since F(U) inhabited might not imply F(U --> T) inhabited. Seems like I answered too hastily. :-/ | |
| Oct 1, 2020 at 22:28 | comment | added | Zhen Lin | @JoeT If I'm not mistaken the localic reflection of the petit étale topos is the petit Zariski topos, so it does work. But the localic reflection of the gros Zariski topos is something else entirely. (Too many points!) | |
| Oct 1, 2020 at 20:00 | comment | added | user164740 | why doesn't this argument apply to the étale topos? | |
| Oct 1, 2020 at 19:36 | review | Late answers | |||
| Oct 1, 2020 at 19:37 | |||||
| Oct 1, 2020 at 19:27 | review | First posts | |||
| Oct 1, 2020 at 21:22 | |||||
| Oct 1, 2020 at 19:19 | history | answered | Matthias Hutzler | CC BY-SA 4.0 |