Weight Filtrations on Log Crystalline Cohomologies of Families of Open Smooth Varieties (Lecture Notes in Mathematics Book 1959)

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 E 2 -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. Annotation 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 Front Matter....Pages i-xxiii Preliminaries on Filtered Derived Categories and Topoi....Pages 15-53 Weight Filtrations on Log Crystalline Cohomologies....Pages 55-217 Weight Filtrations and Slope Filtrations on Rigid Cohomologies (Summary)....Pages 219-248 Back Matter....Pages 249-266 Yukiyoshi Nakkajima, Atsushi Shiho. Includes Bibliographical References (p. 261-264) And Index.