We introduce rigid syntomic cohomology for strictly semistable log schemes over a complete discrete valuation ring of mixed characteristic 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.
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Veronika Ertl, Kazuki Yamada, Comparison between rigid and crystalline syntomic cohomology for strictly semistable log schemes with boundary. Rend. Sem. Mat. Univ. Padova 145 (2021), pp. 213–291DOI 10.4171/RSMUP/81