Timeline for When are free modules on sheaves of sets quasicoherent?
Current License: CC BY-SA 3.0
8 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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| Apr 6, 2017 at 0:57 | answer | added | Artur Jackson | timeline score: 1 | |
| Mar 4, 2017 at 10:51 | comment | added | Ingo Blechschmidt | Exactly. Yes, it is a scheme since $f$ is a local homeomorphism: For any point of $\mathrm{Ét}(\mathcal{E})$ there is an open neighbourhood $U$ which is homeomorphic to some open subset $V$ of $X$, and $(f^{-1} \mathcal{O}_X)|_U$ corresponds to $(\mathcal{O}_X)|_V$ under this homeomorphism. | |
| Mar 4, 2017 at 10:44 | comment | added | მამუკა ჯიბლაძე | For the latter you view $\operatorname{Ét}(\mathcal{E})$ as a ringed space with $f^{-1}\mathcal O_X$? Is it a scheme? | |
| Mar 4, 2017 at 10:37 | comment | added | Ingo Blechschmidt | Yes, and afterwards we can equip $f_! f^{-1} \mathcal{O}_X$ with the structure of an $\mathcal{O}_X$-module. But we also directly use the versions of these functors for modules instead of abelian groups. | |
| Mar 4, 2017 at 10:29 | comment | added | მამუკა ჯიბლაძე | Concerning $f_! f^{-1} \mathcal{O}_X$, where $f : \operatorname{Ét}(\mathcal{E}) \to X$ is the projection of the étalé space associated to $\mathcal{E}$: do you mean the functors $f_!$ and $f^{-1}$ acting on sheaves of abelian groups? | |
| Mar 4, 2017 at 9:47 | history | asked | Ingo Blechschmidt | CC BY-SA 3.0 |