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 GW(X,I
- ) 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 GrGWp(X,I
- ) of this filtration we prove Hp(GrGWp(X,I
- ))≃CHp(X,μI)/2, where μI is the codimension function of the dualizing complex I
- and CHp(X,μI) denotes the Chow group of μI-codimension p-cycles modulo rational equivalence.