On the maximal unramified quotients of \(p\)-adic étale cohomology groups and logarithmic Hodge--Witt sheaves
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)].
scientific article; zbMATH DE number 2028852