Comparison between rigid and crystalline syntomic cohomology for strictly semistable log schemes with boundary

Abstract

We introduce rigid syntomic cohomology for strictly semistable log schemes over a complete discrete valuation ring of mixed characteristic $(0,p)$ In case a good compactification exists, we compare this cohomology theory to Nekovář–Nizioł’s crystalline syntomic cohomology of the generic fibre. The main ingredients are a modification of Große-Klönne’s rigid Hyodo–Kato theory and a generalization of it for strictly semistable log schemes with boundary.