Nakkajima, Yukiyoshi.
Weight Filtrations on Log Crystalline Cohomologies of Families of Open Smooth Varieties [electronic resource] / by Yukiyoshi Nakkajima, Atsushi Shiho. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2008. - online resource. - Lecture Notes in Mathematics, 1959 0075-8434 ; . - Lecture Notes in Mathematics, 1959 .
Preliminaries on Filtered Derived Categories and Topoi -- Weight Filtrations on Log Crystalline Cohomologies -- Weight Filtrations and Slope Filtrations on Rigid Cohomologies (Summary).
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.
9783540705659
10.1007/978-3-540-70565-9 doi
Mathematics.
Geometry, algebraic.
Algebra.
Mathematics.
Algebraic Geometry.
Commutative Rings and Algebras.
QA564-609
516.35
Weight Filtrations on Log Crystalline Cohomologies of Families of Open Smooth Varieties [electronic resource] / by Yukiyoshi Nakkajima, Atsushi Shiho. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2008. - online resource. - Lecture Notes in Mathematics, 1959 0075-8434 ; . - Lecture Notes in Mathematics, 1959 .
Preliminaries on Filtered Derived Categories and Topoi -- Weight Filtrations on Log Crystalline Cohomologies -- Weight Filtrations and Slope Filtrations on Rigid Cohomologies (Summary).
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.
9783540705659
10.1007/978-3-540-70565-9 doi
Mathematics.
Geometry, algebraic.
Algebra.
Mathematics.
Algebraic Geometry.
Commutative Rings and Algebras.
QA564-609
516.35