one can glue the rigid dualizing complexes that its affine pieces have, and obtain a rigid dualizing complex . Once one establishes a global existence of a rigid dualizing complex, given a map of schemes over , one can define , where for a scheme , we set . Dualizing Complex Examples Dualizing Complex for a Projective Variety The dualizing complex for a projective variety is given by the complex Plane Intersecting a Line Consider the projective variety We can compute using a resolution by locally free sheaves. This is given by the complex Since we have that This is the complex See also Verdier duality Notes References Topological methods of algebraic geometry Sheaf theory Duality theories