Crystalline cohomology of algebraic stacks and Hyodo-Kato cohomology
Author(s)
Bibliographic Information
Crystalline cohomology of algebraic stacks and Hyodo-Kato cohomology
（Astérisque, 316）
Société mathématique de France, 2007
Available at / 16 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science数学
叢書/SO 13/3162080187133
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Note
Abstract in French and English
Includes bibliographical references (p. [403]-408) and indexes
Description and Table of Contents
Description
In this text the author uses stack-theoretic techniques to study the crystalline structure on the de Rham cohomology of a proper smooth scheme over a p-adic field and applications to p-adic Hodge theory. He develops a general theory of crystalline cohomology and de Rham-Witt complexes for algebraic stacks and applies it to the construction and study of the ([phi], N, G)-structure on de Rham cohomology. Using the stack-theoretic point of view instead of log geometry, he develops the ingredients needed to prove the Cst-conjecture using the method of Fontaine, Messing, Hyodo, Kato, and Tsuji, except for the key computation of p-adic vanishing cycles. He also generalizes the construction of the monodromy operator to schemes with more general types of reduction than semistable and proves new results about tameness of the action of Galois on cohomology.
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