A note on Gersten's conjecture for logarithmic Hodge-Witt sheaves
type: Item
instance of: scholarly article
title: A note on Gersten's conjecture for logarithmic Hodge-Witt sheaves
zbMATH Open document ID: 0838.14014
DOI: 10.1007/BF00961667
author: Noriyuki Suwa
published in: \(K\)-Theory
publication date: 1996-05-30T00:00:00Z
review text: Let \(X\) be a smooth algebraic scheme over a perfect field \(k\) of characteristic \(p > 0\). Any time we are provided with purity theorems for logarithmic Hodge-Witt sheaves \(W_* \Omega^\bullet_{X, \log}\) the Cousin complex, canonically associated with these sheaves, yields a Gersten resolution of \(R^m \eta^* W_n \Omega^i_{X, \log}\) where \(\eta : X_{et} \to X_{Zar}\). In this paper a proof for the case of \(m = 1\) and \(i = \dim (X)\) is given, by showing local cohomological purity of \(W_n \Omega^i_{X, \log}\). Finally, some standard applications to the study of the \(p\)-primary part of \(K\)-cohomology are explained, in particular: finiteness of \(p\)-torsion of zero-cycles.
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 14M12
Mathematics Subject Classification ID: 14G15
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 19E08
zbMATH DE Number: 790463
zbMATH Keywords: Gersten's conjecture
zbMATH Keywords: characteristic \(p\)
zbMATH Keywords: finiteness of \(p\)-torsion of zero-cycles
zbMATH Keywords: purity theorems for logarithmic Hodge-Witt sheaves
zbMATH Keywords: Cousin complex
Wikidata QID: Q122867510
reviewed by: Luca Barbieri-Viale
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 790463