= Sheaf cohomology under a closed inclusion
{title2=$H^i(Y,i_*\mathcal F)\cong H^i(X,\mathcal F)$}
For a closed inclusion $i:X\hookrightarrow Y$, <direct image sheaf> formation is exact: stalks on $X$ are unchanged and stalks outside $X$ are zero. It also preserves <flasque sheaves>. Pushing forward a <flasque resolution> thus gives a resolution computing cohomology on $Y$, and its complex of <global sections> is identical to the original one on $X$. This proves the displayed isomorphism in every nonnegative degree.
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