A motivic integral $p$-adic cohomology

Logarithmic motivic homotopy theory

“…We further amplify this viewpoint by focusing on non-A 1 -invariant theories such as prismatic cohomology, logarithmic topological Hochschild homology, and cyclic variants thereof. Motivic integral p-adic cohomology defined recently by Merici [58] using log de Rham-Witt sheaves and our work on log-étale motives gives another example.…”

“…In the setting of logarithmic motives, Merici [58] constructed a p-adic realization functor logDM eff lét (k) → D(W (k)) op to the opposite derived ∞-category of W (k)-modules for all field k, by showing that log de Rham-Witt sheaves admit log transfer structures.…”