A graded Gersten-Witt complex for schemes with a dualizing complex and the Chow group
type: Item
instance of: scholarly article
title: A graded Gersten-Witt complex for schemes with a dualizing complex and the Chow group
zbMATH Open document ID: 1127.19005
author: Stefan G. Gille
published in: Journal of Pure and Applied Algebra
publication date: 2007-02-02T00:00:00Z
review text: 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 \(I\).
reviewed by: Stefan Müller-Stach
Mathematics Subject Classification ID: 19G12
Mathematics Subject Classification ID: 14C25
zbMATH DE Number: 5121382
zbMATH Keywords: Gersten-Witt complex
zbMATH Keywords: Chow group
MaRDI profile type: Publication
full work available at URL: j.jpaa.2006.01.004
OpenAlex ID: W2033889848
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DOI: 10.1016/J.JPAA.2006.01.004
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description: scientific article; zbMATH DE number 5121382