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1 vote
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coherent sheaves

suppose $X$ is a smooth variety, with a finite open covering $U_i, i=1,....,k$. $F$ and $G$ are coherent sheaves on $X$, and $G$ is locally free. Suppose on each $U_i$, there is a sheaf morphism $h_i …
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3 votes
3 answers
802 views

Restriction of sheaf

Suppose $X$ is a smooth variety and $F$ is a locally free sheaf on $X$. Let $U$ be an open subset of $X$ and $i$ denote the inclusion map. Is $i_*i^*F$ equal to $F$?
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