Comparison between rigid syntomic 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 generalisation of it for strictly semistable log schemes with boundary.

46 pages, Replaced version: axiomatized the construction of canonical rigid complexes, and modified typos and confusing explanations. To be published in: Rend. Sem. Mat. Univ. Padova \c{opyright} European Mathematical Society