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arXiv · 2211.14303

A motivic integral $p$-adic cohomology

Alberto Merici
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Abstract

We construct an integral $p$-adic cohomology that compares with rigid cohomology after inverting $p$. Our approach is based on the log-Witt differentials of Hyodo-Kato and log-\'etale motives of Binda-Park-{\O}stv{\ae}r. In case $k$ satisfies resolutions of singularities, we moreover prove that it agrees with the "good" integral $p$-adic cohomology of Ertl-Shiho-Sprang: from this we deduce some interesting motivic properties and a K\"unneth formula for the $p$-adic cohomology of Ertl-Shiho-Sprang.

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Alberto Merici. 2022-11-25. A motivic integral $p$-adic cohomology. https://doi.org/10.2140/akt.2025.10.473

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