On the maximal unramified quotients of \(p\)-adic étale cohomology groups and logarithmic Hodge--Witt sheaves
type: Item
instance of: scholarly article
title: On the maximal unramified quotients of \(p\)-adic étale cohomology groups and logarithmic Hodge--Witt sheaves
zbMATH Open document ID: 1092.14503
author: Takeshi Tsuji
published in: Documenta Mathematica
publication date: 2004-01-19T00:00:00Z
full work available at URL: https://eudml.org/doc/52495
full work available at URL: tsuji.dm.html
review text: Summary: Let \(O_K\) be a complete discrete valuation ring of mixed characteristic \((0,p)\) with perfect residue field. From the semi-stable conjecture (\(C_{st}\)) and the theory of slopes, we obtain isomorphisms between the maximal unramified quotients of certain Tate twists of \(p\)-adic étale cohomology groups and the cohomology groups of logarithmic Hodge-Witt sheaves for a proper semi-stable scheme over \(O_K\). The object of this paper is to show that these isomorphisms are compatible with the symbol maps to the \(p\)-adic vanishing cycles and the logarithmic Hodge-Witt sheaves, and that they are compatible with the integral structures under certain restrictions. We also treats an open case and a proof of \(C_{st}\) in such a case is given for that purpose. The results are used in the work of \textit{U. Jannsen} and \textit{S. Saito} [Doc. Math., J. DMV Extra Vol., 479--538 (2003; Zbl 1092.14503)].
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 14F20
zbMATH DE Number: 2028852
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2028852