Hochschild homology of mod-$p$ motivic cohomology over algebraically closed fields

Abstract: We perform Hochschild homology calculations in the algebro-geometric setting of motives. The motivic Hochschild homology coefficient ring contains torsion classes which arise from the mod-$p$ motivic Steenrod algebra and from generating functions on the natural numbers with finite non-empty support. Under the Betti realization, we recover B\"okstedt's calculation of the topological Hochschild homology of finite prime fields.