Weight Filtrations on Log Crystalline Cohomologies of Families of Open Smooth Varieties

In this volume, the authors construct a theory of weights on the log crystalline cohomologies of families of open smooth varieties in characteristic p>0, by defining and constructing four filtered complexes. Fundamental properties of these filtered complexes are proved, in particular the p-adic purity, the functionality of three filtered complexes, the weight-filtered base change formula, the weight-filtered Künneth formula, the weight-filtered Poincaré duality, and the E₂-degeneration of p-adic weight spectral sequences. In addition, the authors state some theorems on the weight filtration and the slope filtration on the rigid cohomology of a separated scheme of finite type over a perfect field of characteristic p>0.

• Cohomology
• Filtered Künneth formula
• Filtered base change formula
• Weight-filtered complexes
• p-adic purity
• p-adic weight filtration

• Department of Mathematics, Tokyo Denki University, Tokyo, Japan

  Yukiyoshi Nakkajima

• Graduate School of Mathematical Sciences, University of Tokyo, Tokyo, Japan

  Atsushi Shiho

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