Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
An integral version of the Hyodo-Kato isomorphism
Let O_K be a complete mixed characteristic DVR with perfect residue field, and let X be a proper formal semistable family over O_K. Answering a question of Fontaine and Jannsen, a classical theorem of Hyodo and Kato provides 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. Using a log variant of the saturated de-Rham-Witt complex of Bhatt, Lurie, and Mathew we prove that such a comparison holds integrally. If time permits, we will explain how this result can be extended to coefficients, using a prismatic interpretation of crystalline cohomology relative to a base without a \delta-ring structure. The results are part of joint works with Shuji Saito (Tokyo).
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