Semistable conjecture via k-theory: integral case

Nizio l proved a p-adic comparison isomorphism of semistable schemes via K-theory. In this paper, we generalize it to integral setting; to make the classical argument work, we need the Gysin map and Grothendieck-Riemann-Roch in the log crystalline setting, and we generalize the method of Berthelot, and Gillet-Messing, respectively.