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

  • Veronika Ertl

    Universität Regensburg, Germany
  • Kazuki Yamada

    Keio University, Yokohama, Japan
Comparison between rigid and crystalline syntomic cohomology for strictly semistable log schemes with boundary cover
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Abstract

We introduce rigid syntomic cohomology for strictly semistable log schemes over a complete discrete valuation ring of mixed characteristic (0,p)(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.

Cite this article

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. 213–291

DOI 10.4171/RSMUP/81