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A graded Gersten-Witt complex for schemes with a dualizing complex and the Chow group. (English) Zbl 1127.19005
For every scheme \(X\) with a dualizing complex \(I_\bullet\) a Gersten-Witt complex \(GW(X,I_\bullet)\) is constructed. It carries a natural filtration by the fundamental ideal \(I\). In a Bloch-Ogus type way this implies as the main theorem a comparison statement between codimension \(p\) Chow groups mod 2 and the \(p\)th cohomology of the \(p\)th graded quotient of such Gersten-Witt complexes. This work extends and complements work of Rost, Balmer, Walker and Pardon and is related but independent of the proof of the Milnor conjecture by Voevodsky. The methods include a construction of generalized residue maps preserving in a suitable way the filtration by powers of \(I\).

MSC:
19G12 Witt groups of rings
14C25 Algebraic cycles
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