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This analysis reveals a connection between tame motives and log-étale motives, suggesting implications for motivic cohomology.
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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Alberto Merici (2025) studied this question.
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