A graded Gersten-Witt complex for schemes with a dualizing complex and the Chow group |
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Authors: | Stefan Gille |
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Affiliation: | Mathematisches Institut, Universität München, Theresienstrasse 39, 80333 München, Germany |
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Abstract: | 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 μI is the codimension function of the dualizing complex I• and denotes the Chow group of μI-codimension p-cycles modulo rational equivalence. |
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Keywords: | Primary, 19G12 secondary, 14C25 |
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