Timeline for Sheaves and gratings
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 12, 2023 at 15:32 | vote | accept | coudy | ||
| Jul 12, 2023 at 15:23 | comment | added | coudy | @SimonWadsley Yes, I must have read too much in the paper. Thanks. | |
| Jul 12, 2023 at 15:19 | comment | added | Simon Wadsley | I think he says global sections is what he has in mind: (copy and pasted with minor editing) "Inversement~ tout faisceau $F$ définit une carapace, à savoir le module des sections $\Gamma(F)$ . En effet, dans l’exposé 14 (numéro 1) on a défini des supports dans $\Gamma(F)$ ; et on vérifie aussitôt que les axiomes d’une carapace sont remplis. Pour tout faisceau $F$ et toute famille $\Phi$, $\Gamma_{\Phi}(F)$ est carapace." | |
| Jul 12, 2023 at 15:10 | comment | added | coudy | @NicolasHemelsoet Yes, but then I guess this construction gives the module of global sections. Which probably is what Cartan had in mind. | |
| Jul 12, 2023 at 15:03 | comment | added | Nicolas Hemelsoet | If you take the subset of the product consistued of "coherent sections" then property 1 seems to work no? The projection is the obvious one if $x \in U$ and 0 else. | |
| Jul 12, 2023 at 15:00 | comment | added | coudy | Yes, this is the translation used by Cartan. Grating is the term used by Alexander in his 1938 paper and Cartan used the same term in his 1949 course for a slightly more general concept. The definition of carapace given in the linked seminar matches the definition of a grating given in his course. | |
| Jul 12, 2023 at 14:59 | history | edited | LSpice | CC BY-SA 4.0 |
(pre)- -> (pre-); name of seminar; `\cal` -> `\mathcal`
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| Jul 12, 2023 at 14:58 | comment | added | LSpice | Is 'grating' really the standard translation? Google thinks, with no context, that 'carapace' means 'shell', so it seems like 'shelling' might make more sense. | |
| Jul 12, 2023 at 14:28 | answer | added | Simon Wadsley | timeline score: 3 | |
| Jul 12, 2023 at 9:59 | history | edited | coudy | CC BY-SA 4.0 |
Correct typo
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| Jul 12, 2023 at 8:25 | comment | added | coudy | @NicolasHemelsoet What would be the projection ${\cal F}(U) \mapsto {\cal F}_x$? Also I don't think that point 1 would hold. | |
| Jul 11, 2023 at 18:34 | comment | added | Nicolas Hemelsoet | Why not product of $F(U)$ over all $U$? | |
| Jul 11, 2023 at 17:19 | history | asked | coudy | CC BY-SA 4.0 |