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PreprintCC BY 4.0arXiv

An integral Hyodo--Kato isomorphism

  • Federico Binda
  • Shuji Saito
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Abstract

Let 𝒪K be a mixed characteristic complete DVR with perfect residue field k, and let X be a proper formal scheme over 𝒪K with semistable reduction. Answering a question of Fontaine and Jannsen, a classical theorem of Hyodo and Kato gives a rational identification between the log crystalline cohomology of the special fiber X0 over W(k)0 with the de Rham cohomology of the generic fiber XK. In this note, we use a log variant of the saturated de Rham--Witt complex of Bhatt--Lurie--Mathew to prove that such a comparison holds integrally.

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Cite

BibTeXRIS
BibTeX
@misc{binda2026integral,
  title = {{An integral Hyodo--Kato isomorphism}},
  author = {Federico Binda and Shuji Saito},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00723},
  eprint = {2609.00723},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00723},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An integral Hyodo--Kato isomorphism
AU  - Federico Binda
AU  - Shuji Saito
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00723
UR  - https://arxiv.org/abs/2609.00723
AB  - Let 𝒪_K be a mixed characteristic complete DVR with perfect residue field k, and let X be a proper formal scheme over 𝒪_K with semistable reduction. Answering a question of Fontaine and Jannsen, a classical theorem of Hyodo and Kato gives a rational identification between the log crystalline cohomology of the special fiber X_0 over W(k)^0 with the de Rham cohomology of the generic fiber X_K. In this note, we use a log variant of the saturated de Rham--Witt complex of Bhatt--Lurie--Mathew to prove that such a comparison holds integrally.
ER  -