\(p\)-adic Hodge theory for open varieties (Q650850)

This note is an announcement of the author's results concerning the comparison theorems in \(p\)-adic Hodge theory (Fontaine-Jannsen's \(\mathrm{C}_{\mathrm{st}}\) conjecture) for open varieties. The preprint ``\(p\)-adic étale cohomology and crystalline cohomology for open varieties with semistable reduction'' that contains the full proof was still under review as this note was published. The ingredients of the proof are syntomic cohomology and logarithmic geometry, more precisely ``hollow log schemes''.