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Jul 21, 2022 at 14:49 comment added David Loeffler He's talking about the correspondence between vector bundles on $X$ and locally free sheaves of $O_X$-modules (and being cavalier by omitting the words "locally free"). See e.g. this careful writeup: huettenhain.net/written/scripts/vector-bundles.pdf
Jul 21, 2022 at 14:48 comment added user164898 en.wikipedia.org/wiki/Serre%E2%80%93Swan_theorem
Jul 21, 2022 at 14:42 history asked Abel CC BY-SA 4.0