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

  • Yukiyoshi Nakkajima
  • Atsushi Shiho

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

  • Yukiyoshi Nakkajima
    • 1
  • Atsushi Shiho
    • 2
  1. 1.Department of MathematicsTokyo Denki UniversityTokyoJapan
  2. 2.Graduate School of Mathematical SciencesUniversity of TokyoTokyoJapan

Bibliographic information