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.

List of contents

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

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.

Product details

• Authors: Yukiyosh Nakkajima, Yukiyoshi Nakkajima, Atsushi Shiho
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 23.02.2011
• EAN: 9783540705642
• ISBN: 978-3-540-70564-2
• No. of pages: 272
• Dimensions: 148 mm x 237 mm x 17 mm
• Weight: 432 g
• Illustrations: X, 272 p.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, B, Geometrie / Algebraische Geometrie, Algebraische Geometrie, Cohomology; Filtered Künneth formula; Filtered base change formula; Weight-filtered complexes; p-adic purity; p-adic weight filtration, Mathematics and Statistics, Algebraic Geometry, Commutative algebra, Commutative rings, Commutative Rings and Algebras