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Global section functor

Section functor with support

Local cohomology

For $U=X\setminus Z$, local and ordinary <sheaf cohomology> fit into the natural sequence
$$
\cdots\to H^{i-1}(U,\mathcal F|_U)
\to H_Z^i(X,\mathcal F)
\to H^i(X,\mathcal F)
\to H^i(U,\mathcal F|_U)
\to H_Z^{i+1}(X,\mathcal F)\to\cdots.
$$

Long exact sequence for local cohomology

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 113 / 4 / c / Solution

Long exact sequence for local cohomology

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Long exact sequence for local cohomology

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