Timeline for Is an infinite direct sum of quasi-coherent $\mathcal{O}_X$-modules quasi-coherent on a complex manifold?
Current License: CC BY-SA 4.0
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| Aug 19, 2023 at 16:29 | comment | added | Jason Starr | Just to clarify, Gabber constructs a quasi-coherent sheaf that is isomorphic to a direct sum of countably many copies of the structure sheaf on either $X\setminus \{p\}$ or $X\setminus\{q\}$. | |
| Aug 19, 2023 at 11:21 | comment | added | Jason Starr | That is not true. Gabber constructs a (nonzero) quasi-coherent sheaf $\mathcal{F}(p,q)$ on the open unit disk $X$ in the complex plane that has vanishing global sections on every open disk containing both $p$ and $q$. Now let $(p_n)$ and $(q_n)$ be sequences of points in the punctured unit disk that limit to zero. The direct sum of the sheaves $\mathcal{F}(p_n,q_n)$ is globally generated on no open disk containing zero. | |
| Aug 18, 2023 at 22:52 | history | asked | Zhaoting Wei | CC BY-SA 4.0 |