Reference. Motivic $p$-adic tame cohomology [merici2025tame]

We construct a comparison functor between (\mathbf A^1-local) tame motives and (\overline\square -local) log-étale motives over a field \k\ of positive characteristic. This generalizes Binda–Park–Østvær’s comparison for the Nisnevich topology. As a consequence, we construct an \E_ınfty-ring spectrum \H\mathbb Z/p^m\ representing mod \p^m\ 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.

@article{mericiMotivicPadicTame2025,
  title = {Motivic \$p\$-Adic Tame Cohomology},
  author = {Merici, Alberto},
  year = 2025,
  journal = {Bulletin of the London Mathematical Society},
  volume = {57},
  number = {10},
  pages = {3194--3210},
  issn = {1469-2120},
  doi = {10.1112/blms.70151},
}