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Crystalline Cohomology of Algebraic Stacks and Hyodo-Kato Cohomology

Martin C. Olsson

出版	Société Mathématique de France, 2007
主題	Mathematics / Geometry / AlgebraicMathematics / Topology
ISBN	28562924969782856292495
URL	http://books.google.com.hk/books?id=Ch4ZAQAAIAAJ&hl=&source=gbs_api

註釋

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 $(\varphi, N, G)$-structure on de Rham cohomology. Using the stack-theoretic point of view instead of log geometry, he develops the ingredients needed to prove the $C_{\text {st}}$-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.