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Let $X$ be a topological space (I'm interested in the case of $X$ being a complex algebraic variety with the Zariski topology) and $Z$ a constructible subset (i.e. a finite union of locally closed sets).

If $F$ is a sheaf of abelian groups on $X$, is there a useful notion of local cohomology of $F$ with supports in $Z$?

This should reduce to the usual definition of $H^i_Z(X, F)$ when $Z$ is locally closed.

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