A graded Gersten-Witt complex for schemes with a dualizing complex and the Chow group

We construct for any scheme X with a dualizing complex I_• a Gersten-Witt complex and show that the differential of this complex respects the filtration by the powers of the fundamental ideal. To prove this we introduce second residue maps for one-dimensional local domains which have a dualizing complex. This residue maps generalize the classical second residue morphisms for discrete valuation rings. For the cohomology of the quotient complexes of this filtration we prove , where μ_I is the codimension function of the dualizing complex I_• and denotes the Chow group of μ_I-codimension p-cycles modulo rational equivalence.