Weight filtrations on log crystalline cohomologies of families of open smooth varieties (Lecture Notes in Mathematics)

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.

Preliminaries on Filtered Derived Categories and Topoi.- Weight Filtrations on Log Crystalline Cohomologies.- Weight Filtrations and Slope Filtrations on Rigid Cohomologies (Summary).