local cohomology

Local cohomology is a mathematical concept from algebraic geometry and commutative algebra. It helps mathematicians understand the properties of shapes (or spaces) that are 'near' a specific point or ideal. By focusing on local neighborhoods, it refines our understanding of functions and their behaviors in these areas. Essentially, it allows us to study how structures behave in a localized context, revealing insights that might be lost when looking at the entire space. This approach is valuable for solving problems related to singularities, intersections, and local properties of various mathematical objects.