On the maximal unramified quotients of pp-adic étale cohomology groups and logarithmic Hodge--Witt sheaves

  • Takeshi Tsuji

Abstract

Let OKO_K be a complete discrete valuation ring of mixed characteristic (0,p)(0,p) with perfect residue field. From the semi-stable conjecture (CstC_{st}) and the theory of slopes, we obtain isomorphisms between the maximal unramified quotients of certain Tate twists of pp-adic étale cohomology groups and the cohomology groups of logarithmic Hodge-Witt sheaves for a proper semi-stable scheme over OKO_K. The object of this paper is to show that these isomorphisms are compatible with the symbol maps to the pp-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 CstC_{st} in such a case is given for that purpose. The results are used in the work of U. Jannsen and S. Saito [Doc. Math., J. DMV Extra Vol., 479--538 (2003; Zbl 1092.14503)].