On the Maximal Unramified Quotients of p-Adic Étale Cohomology Groups and Logarithmic Hodge–Witt Sheaves Dedicated to Professor K. Kato on his 50th birthday

Let OK be a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field. From the semi-stable conjecture (Cst) 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 OK . The object of this paper is to show that these isomorphisms are compatible with the symbol maps to the padic 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 Cst in such a case is given for that purpose. The results are used in the work of U. Jannsen and S. Saito in this volume. 2000 Mathematics Subject Classification: 14F30, 14F20