A motivic integral $p$-adic cohomology

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-étale motives of Binda-Park-Østvær. 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 Künneth formula for the $p$-adic cohomology of Ertl-Shiho-Sprang.

Accepted for publication in the Annals of K-Theory

References in corpus (1)

• The tame site of a scheme