Local cohomology is a concept in algebraic geometry and commutative algebra that extends the notion of ordinary cohomology to study the local behavior of a module over a ring, particularly with respect to a specified ideal. It is particularly useful for understanding the properties of sheaves and modules around points in a space or in relation to certain subvarieties.
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Local cohomology consists of the right derived functors of the section functor with support. It measures sections and cohomology concentrated along a closed subset .