Timeline for Existence of rigid objects in the derived category of a smooth projective variety
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 27, 2022 at 16:48 | vote | accept | Libli | ||
| Jul 27, 2022 at 16:47 | vote | accept | Libli | ||
| Jul 27, 2022 at 16:48 | |||||
| Jul 27, 2022 at 15:22 | answer | added | Jason Starr | timeline score: 1 | |
| Jul 27, 2022 at 14:31 | comment | added | Libli | @JasonStarr : very interesting! Do you think you could make an answer out of your argument? | |
| Jul 27, 2022 at 10:16 | comment | added | Jason Starr | The argument I have in mind applies to Abelian varieties of arbitrary dimension, | |
| Jul 27, 2022 at 6:05 | comment | added | Libli | @JasonStarr : That may be. On the other hand, I know prove in the edit that any non zero object on an elliptic curve has non vanishing Ext^1. This seems however very specific to the case of curve ( because then $Coh(X)$ is hereditary) and I have added an extra hypothesis on $ \dim X$ to improve my question. | |
| Jul 27, 2022 at 0:12 | comment | added | Jason Starr | If you consider the "filtration" by good truncations, I believe that every rigid object on an elliptic curve is quasi-isomorphic to zero. | |
| Jul 26, 2022 at 21:27 | history | edited | Libli | CC BY-SA 4.0 |
Edits following Johan comment
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| Jul 26, 2022 at 21:19 | comment | added | Libli | @JasonStarr : good point! This is why I asked that, ideally, the Chern character would be non zero. | |
| Jul 26, 2022 at 21:13 | comment | added | Jason Starr | The zero object is rigid. | |
| Jul 26, 2022 at 21:07 | history | edited | Libli | CC BY-SA 4.0 |
deleted 46 characters in body
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| Jul 26, 2022 at 20:37 | history | edited | Libli | CC BY-SA 4.0 |
added 499 characters in body
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| Jul 26, 2022 at 19:18 | comment | added | Johan | Hint: elliptic curve. | |
| Jul 26, 2022 at 18:04 | history | asked | Libli | CC BY-SA 4.0 |