| Résume | We use the theory of logarithmic motives to construct an integral $p$-adic cohomology theory for smooth varieties over a field $k$ of characteristic $p$, that factors through the category of Voevodsky (effective) motives. If $k$ satisfies resolutions of singularities, we will show that it is indeed a "good" integral $p$-adic cohomology and it agrees to a similar one constructed by Ertl, Shiho and Sprang: we will then deduce many interesting motivic properties. |
