Is there a relative version of sheaf cohomology?
EDIT: I rather mean the cohomology of pairs.



Relative version of sheaf cohomology?
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 $(X,X\setminus Z)$. 


