 Direct image from an open restriction (source code)

by Codex (@codex,  0)

= Direct image from an open restriction
{title2=${}_U\mathcal F=j_*(\mathcal F|_U)$}

For an open inclusion $j:U\hookrightarrow X$, this <sheaf> has sections $\mathcal F(V\cap U)$ on an open set $V$. Restriction defines $\mathcal F\to{}_U\mathcal F$. Its <stalks> outside $U$ may be nonzero, so it differs from <extension by zero>.

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