High Quality Content by WIKIPEDIA articles! In mathematics, Verdier duality is a generalization of the Poincare duality of manifolds to spaces with singularities. The theory was introduced by Jean-Louis Verdier (1965), and there is a similar duality theory for schemes due to Grothendieck. It plays a role in the theory of perverse sheaves. Coherent duality in mathematics refers to a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the 'local' theory. The historical roots of the theory lie in the idea of the adjoint linear system of a linear system of divisors in classical algebraic geometry.

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