Verdier duality is a concept from the field of algebraic geometry and consists of a duality theory for sheaves on a topological space, particularly in the context of schemes and general sheaf theory. It is named after Jean-Louis Verdier, who developed this theory in the context of derived categories. At its core, Verdier duality provides a way to define a duality between certain categories of sheaves.
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On bounded constructible complexes over locally compact stratified spaces, Verdier duality is , where is the dualizing complex. For an oriented real -manifold, . Proper direct image commutes with this duality, and . These properties exchange stalk support conditions with costalk conditions.