$X$ is quasi-separated and for every quasi-coherent sheaf $\mathcal{F}$ of finite type on $X$ there exist integers $n > 0$, $k \geq 0$ such that $\mathcal{F}$ is a quotient of a direct sum of $k$ copies of $\mathcal{L}^{\otimes - n}$, and
$X$ is quasi-separated and for every quasi-coherent sheaf $\mathcal{F}$ of finite type on $X$ there exist integers $n > 0$, $k \geq 0$ such that $\mathcal{F}$ is a quotient of a direct sum of $k$ copies of $\mathcal{L}^{\otimes - n}$, and
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