August 15, 2025Open Access

Motivic pp‐adic tame cohomology

Key Points

A comparison functor is constructed linking tame motives and log-étale motives, enhancing our understanding of cohomological relationships.
This study results in the creation of a ring spectrum that represents mod tame motivic cohomology, enriching the framework of motives.
The existence of this ring spectrum leads to important findings on tame motivic cohomology and log-étale motives.
Supports theoretical advancements in algebraic geometry and enriches comparisons within motivic cohomology.

Abstract

Abstract We construct a comparison functor between (‐local) tame motives and (‐local) log‐étale motives over a field of positive characteristic. This generalizes Binda–Park–Østvær's comparison for the Nisnevich topology. As a consequence, we construct an ‐ring spectrum representing mod tame motivic cohomology: the existence of this ring spectrum and the usual properties of motives imply some results on tame motivic cohomology and a comparison with log étale motivic cohomology.

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