Alberto Merici (Oslo)

Abstract: 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.
If time permits, we will explain how the above construction suggests a strategy to prove a conjecture of Hübner and Schmidt on tame motivic cohomology.