Lemma 38.39.1 (0EXB)—The Stacks project

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Part 2: Schemes
Chapter 38: More on Flatness
Section 38.39: Descent vector bundles in positive characteristic
Lemma 38.39.1 (cite)

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Lemma 38.39.1. Let $p$ be a prime number. Let $S$ be a quasi-compact and quasi-separated scheme over $\mathbf{F}_ p$ . The category $\mathop{\mathrm{colim}}\nolimits _ F \textit{Vect}(S)$ is equivalent to the category of finite locally free modules over the sheaf of rings $\mathop{\mathrm{colim}}\nolimits _ F \mathcal{O}_ S$ on $S$ .

Proof. Omitted. $\square$

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