For $X$ a smooth, projective variety one has that for two coherent sheaves $\mathcal{F}$ and $\mathcal{G}$, $\mathrm{Ext}^i(\mathcal{F},\mathcal{G})=0$, for $i>>0$. Do we really need projectivity of $X$ or does this hold also for quasi-projective varieties? I somehow feel that smooth is enough...
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