Real Topological Hochschild Homology of Perfectoid Rings

TL;DR

This paper refines existing results to compute the real topological Hochschild homology (THR) of perfectoid rings, aiding in motivic filtration studies and establishing a real version of the Hochschild-Kostant-Rosenberg theorem.

Contribution

It provides the first computation of THR for perfectoid rings and introduces a real refinement of the Hochschild-Kostant-Rosenberg theorem.

Findings

Computed THR of perfectoid rings.

Established a real Hochschild-Kostant-Rosenberg theorem.

Facilitated motivic filtration analysis on quasisyntomic rings.

Abstract

We refine several results of Bhatt-Morrow-Scholze on THH to THR. In particular, we compute 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.