A motivic integral p-adic cohomology

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-étale motives of Binda–Park–Østvær. In case $k$ satisfies resolution 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 Künneth formula for the $p$ -adic cohomology of Ertl–Shiho–Sprang.

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Keywords

motivic, $p$-adic, tame

Mathematical Subject Classification

Primary: 14F30

Secondary: 14F42, 19E15

Milestones

Received: 31 March 2025

Revised: 2 June 2025

Accepted: 10 July 2025

Published: 29 July 2025

Authors

Alberto Merici
Institut für Mathematik Universität Heidelberg Heidelberg Germany

Vol. 10, No. 3, 2025

Alberto Merici

Abstract

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Keywords

Mathematical Subject Classification

Milestones

Authors