sentences:  Taking global sections of both sides in the local statement gives global Verdier duality.The dualizing complex formula_12 on formula_5 is defined to be
  
  where "p" is the map from formula_5 to a point.Part of what makes Verdier duality interesting in the singular setting is that when formula_5 is not a manifold (a graph or singular algebraic variety for example) then the dualizing complex is not quasi-isomorphic to a sheaf concentrated in a single degree.