La conjecture de Gersten pour les faisceaux de Hodge-Witt logarithmique. (The Gersten conjecture for the logarithmic Hodge-Witt sheaves)
type: Item
instance of: scholarly article
title: La conjecture de Gersten pour les faisceaux de Hodge-Witt logarithmique. (The Gersten conjecture for the logarithmic Hodge-Witt sheaves)
zbMATH Open document ID: 0715.14011
DOI: 10.1215/S0012-7094-88-05727-4
author: Michel Gros
author: Noriyuki Suwa
published in: Duke Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: Let X be a smooth scheme over a perfect field k of characteristic \(p>0,\) \(W_ n\Omega^ i_{X,\log}\) be the logarithmic abelian étale Hodge-Witt sheaf, \(\epsilon: X_{et}\to X_{zar}\) be the projection of the étale topos onto the Zariski topos. For every \(m>0\), the authors constructs a flat resolution of the sheaf \(R^ m\epsilon_*W_ n\Omega^ i_{X,\log}\) in the Zariski topology. From this, in particular, the equality \(R^ m\epsilon_*W_ n\Omega^ i_{X,\log}=0\) follows for all \(m>1\). In view of the notation \({\mathcal H}^ r({\mathbb{Z}}/p^ n{\mathbb{Z}}(i))=R^{r-1}\epsilon_*W_ n\Omega^ i_{X,\log}\), the authors note that the constructed resolution is analogous in the case \(m=0\) to the corresponding Bloch-Ogus resolution for the \(\ell\)-adic sheaves \({\mathcal H}^ r({\mathbb{Z}}/\ell^ n{\mathbb{Z}}(i))\) in the case \(\ell \neq p\) and allows one to obtain the ``Bloch-Quillen formula modulo \(p^ n{}'': CH^ d(X)/p^ n\overset \sim \rightarrow H^ d(X_{zar},{\mathcal H}^ d({\mathbb{Z}}/p^ n{\mathbb{Z}}(d))\).
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14C30
zbMATH DE Number: 4177251
zbMATH Keywords: characteristic p
zbMATH Keywords: logarithmic abelian étale Hodge-Witt sheaf
MaRDI profile type: Publication
cites work: \(p\)-adic étale cohomology
cites work: Gersten's conjecture and the homology of schemes
cites work: Classes de Chern et classes de cycles en cohomologie de Hodge-Witt logarithmique
cites work: Application d'Abel-Jacobi p-adique et cycles algébriques. (p-adic Abel- Jacobi map and algebraic cycles)
cites work: Complexe de de\thinspace Rham-Witt et cohomologie cristalline
cites work: Q3739259
cites work: Q4742907
cites work: Values of Zeta Functions of Varieties Over Finite Fields
cites work: Higher algebraic K-theory: I
cites work: Opérations En K-Théorie Algébrique
cites work: Torsion dans le groupe de Chow de codimension deux
cites work: Universal exactness in algebraic K-theory
full work available at URL: s0012-7094-88-05727-4
OpenAlex ID: W1493621599
Recommended article: A note on Gersten's conjecture for logarithmic Hodge-Witt sheaves
Recommended article: Logarithmic Hodge-Witt sheaves on normal crossing varieties
Recommended article: Q3515678
Recommended article: K-theory and logarithmic Hodge-Witt sheaves of formal schemes in characteristic p
Recommended article: Classes de Chern et classes de cycles en cohomologie de Hodge-Witt logarithmique
Recommended article: Q4874026
Recommended article: On logarithmic nonabelian Hodge theory of higher level in characteristic \(p\)
Recommended article: Sur la théorie de Hodge-Deligne. (On the Hodge-Deligne theory)
Recommended article: Degenerations of log Hodge de Rham spectral sequences, log Kodaira vanishing theorem in characteristic \(p>0\) and log weak Lefschetz conjecture for log crystalline cohomologies
Recommended article: Q4407872
description: scientific article; zbMATH DE number 4177251