A graded Gersten-Witt complex for schemes with a dualizing complex and the Chow group
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 \(I\).
scientific article; zbMATH DE number 5121382
scientific article