© 2008

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


Part of the Lecture Notes in Mathematics book series (LNM, volume 1959)

Table of contents

About this book


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.


Cohomology Filtered Künneth formula Filtered base change formula Weight-filtered complexes p-adic purity p-adic weight filtration

Authors and affiliations

  1. 1.Department of MathematicsTokyo Denki UniversityTokyoJapan
  2. 2.Graduate School of Mathematical SciencesUniversity of TokyoTokyoJapan

Bibliographic information

  • Book Title Weight Filtrations on Log Crystalline Cohomologies of Families of Open Smooth Varieties
  • Authors Yukiyoshi Nakkajima
    Atsushi Shiho
  • Series Title Lecture Notes in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-540-70564-2
  • eBook ISBN 978-3-540-70565-9
  • Series ISSN 0075-8434
  • Edition Number 1
  • Number of Pages X, 272
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebraic Geometry
    Commutative Rings and Algebras
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