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

ISBN-13: 9783540705642 / Angielski / Miękka / 2008 / 272 str.

Yukiyoshi Nakkajima;Atsushi Shiho

Opis

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 Kunneth formula, the weight-filtered Poincare 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.

Spis treści

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

Blurb

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.