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arXiv · 2204.00441

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

Bjørn Ian Dundas·Michael A. Hill·Kyle Ormsby·Paul Arne Østvær
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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.

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Bjørn Ian Dundas, Michael A. Hill, Kyle Ormsby, Paul Arne Østvær. 2022-04-01. Hochschild homology of mod-$p$ motivic cohomology over algebraically closed fields. https://arxiv.org/abs/2204.00441

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