Let $X$ be a quasi-projective variety, $Y$ a projective variety, and $f:X \rightarrow Y$ an open immersion. If $\mathcal{F}$ is a locally free coherent sheaf, what can be said about $f_\ast \mathcal{F}$? Is it coherent? Is it torsion free? Is it reflexive?
Is the pushforward of a locally free sheaf by an open immersion coherent?
Yemon Dai
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