Real topological Hochschild homology of perfectoid rings

Abstract

We refine several results of Bhatt–Morrow–Scholze on $\mathrm{THH}$ to real topological Hochschild homology ($\mathrm{THR}$). In particular, we compute $\mathrm{THR}$ of perfectoid rings. This will be useful for establishing motivic filtrations on real topological Hochschild and cyclic homology of quasisyntomic rings. We also establish a real refinement of the Hochschild–Kostant–Rosenberg theorem.