In algebraic topology, one defines relative cohomology groups $H(X,A)$ of a pair of spaces $A\subset X$. Is there an analogue in algebraic geometry of cohomology of a pair of schemes?
For example, let $H$ be either etale or de Rham cohomology theory, let $X$ be a scheme and let $D$ be a divisor on $X$ or a closed subvariety of $X$. Can one define relative cohomology $H^*(X,D)$ of a pair in a useful way ? Under what assumptions?
The simplest example would be $X$ a curve and $D$ is a pair of points.