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Let $F$ be a coherent sheaf on $\mathbb{P}^n$. Why do there exist integers $N$ and $p$ such that there is a surjection $$\mathcal{O}_{\mathbb{P}^n}(p)^{\oplus N}\rightarrow F\rightarrow 0\;?$$

I might be misinterpreting a book, so if the above is false, then what would a similar true statement be?

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    Do you know the theorem of Serre that says for a coherent $F$, there exists some $n_0$ such that for all $n\geq n_0$ we have $F(n)$ is generated by global sections?2012-11-29
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    Deleted previous comments because I was wrong. I must also admit I found a proof of my statement in the same book. I'm terribly sorry!2012-11-29
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    Since I'm new here I don't know what the right way to handle this is. But if necessary this question can be marked as "closed" or something to that effect.2012-11-29
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    Well... Just in case this'll be helpful to someone, the above is corollary 5.4.3 on page 62 (page 36 of the pdf) in George Kempf's book: http://bib.tiera.ru/b/72466.2012-12-11

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