Let $X$ be a projective variety and let $\mathcal{F},\mathcal{G}$ be coherent sheaves on $X$.
If $Ext^{1}(\mathcal{F},\mathcal{G}) = 0$ can one say something about $\mathcal{E}xt^{1}(\mathcal{F},\mathcal{G})$?
Global to local for Ext groups and Sheaves
Puzzled
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