Description

In this texte we study using stack-theoretic techniques the crystalline structure on the de Rham cohomology of a proper smooth scheme oer a p-adic field and applications to p-adic Hodge theory. We develop a general theory of crystalline cohomology and de Rham-Witt complexes for algebraic stacks, and apply it to the construction and study of the (alpha, N, G- structure on de Rham cohomology. Using the stack-theoretic point of view instead of log geometry, we develop the ingredients needed to prove the C_st-conjecture using the method of Fontaine, Messing, Hyodo Kato, and Tsuji, except for the key computation of p-adic vanishing cycles. We also generalize the construction of the monodromy operator to schemes with more general types of reduction than semistable, and prove new results about tameness of the action of Galois on cohomology.