Weight Filtrations on Log Crystalline Cohomologies

In this chapter, we construct a theory of weights of the log crystalline cohomologies of families of open smooth varieties in characteristic p < 0, by constructing four filtered complexes. We prove fundamental properties of these filtered complexes. Especially we prove the p-adic purity, the functoriality of three filtered complexes, the convergence of the weight filtration, the weight-filtered Künneth formula, the weight-filtered Poincaré duality and the E₂-degeneration of p-adic weight spectral sequences. We also prove that our weight filtration on log crystalline cohomology coincides with the one defined by Mokrane in the case where the base scheme is the spectrum of a perfect field of characteristic p < 0.