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 Nekovar-Niziol's crystalline syntomic cohomology of the generic fibre. The main ingredients are a modification of GroBe-Klonne's rigid Hyodo-Kato theory and a generalization of it for strictly semistable log schemes with boundary.