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