| Abstrakt: |
For a proper, smooth scheme X over a p-adic field K , we show that any proper, flat, semistable OK-model X of X whose logarithmic de Rham cohomology is torsion free determines the same OK-lattice inside HdRi(X/K) and, moreover, that this lattice is functorial in X. For this, we extend the results of Bhatt–Morrow–Scholze on the construction and the analysis of an Ainf-valued cohomology theory of p-adic formal, proper, smooth OK-schemes X to the semistable case. The relation of the Ainf -cohomology to the p-adic étale and the logarithmic crystalline cohomologies allows us to reprove the semistable conjecture of Fontaine–Jannsen. [ABSTRACT FROM AUTHOR] |
