On residue complexes, dualizing sheaves and local cohomology modules

According to Grothendieck Duality Theory [RD], on each variety V over a field k, there is a canonical complex of {Mathematical expression}-modules, the residue complex {Mathematical expression}. These complexes satisfy (and are characterized by) functorial properties in the category V of k-varieties. In [Ye] a complex {Mathematical expression} is constructed explicitly (when the field k is perfect). The main result of this paper is that the two families of complexes, {Mathematical expression} and {Mathematical expression}, which carry certain additional data (such as trace maps...), are uniquely isomorphic. As a corollary we recover Lipman's canonical dualizing sheaf of [Li], and we obtain formulas for residues of local cohomology classes of differential forms.