In algebraic topology, relative (co)homology is very useful. For example, we have a long exact sequence which is often helpful for lots of calculations.

In algebraic geometry, we have local cohomology, which is basically the same thing and has the same long exact sequence. However, while the commutative algebra community seems to use this a lot, it seems to be rarely used in algebraic geometry. Is indeed local cohomology more useful in commutative algebra than it is in algebraic geometry? If so, why?

(I'm primarily talking about the Zariski topology, but we also have local cohomology in any context where we have six functors; in étale cohomology, in de Rham cohomology, etc. I would also like to know something about local cohomology in these contexts.)

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