Home Questions Tags Users Unanswered. Equivalence of categories of vector bundles and locally free sheaves Ask Question. Asked 5 years, 7 months ago. Active 1 year, 3 months ago. Viewed 3k times. Irfan Kadikoylu Irfan Kadikoylu 5 5 silver badges 12 12 bronze badges. His exercise about vector bundles is just terrible.
That's a perfectly reasonable expectation; it just turns out to be false.
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Basic example: the ideal sheaf of a point on the line. Martin Brandenburg Martin Brandenburg k 14 14 gold badges silver badges bronze badges. Do you know a reference for vector bundles on schemes? You can just name the book where you learned what you have written above. Last question: Do you fix the open cover and the trivializations in your definition of vector bundle?
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