# Crystalline Cohomology of Algebraic Stacks and Hyodo-Kato Cohomology

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*Martin C. Olsson*

A publication of the Société Mathématique de France

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.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

#### Readership

Graduate students and research mathematicians interested in algebra and algebraic geometry.