TITLE: Relative version of sheaf cohomology?
QUESTION [8 upvotes]: Is there a relative version of sheaf cohomology?
EDIT: I rather mean the cohomology of pairs.

REPLY [6 votes]: It turns out that my previous answer dealt with the wrong question.  The answer to the
new question is also yes:
local cohomology $H\_Z(X,\mathcal F)$ corresponds to cohomology of the pair $(X,X\setminus Z)$.