On the periodic topological cyclic homology of DG categories in characteristic p

TL;DR

This paper establishes an isomorphism between the p-adically completed periodic topological cyclic homology and the periodic cyclic homology of a lifted DG category over Witt vectors in characteristic p, advancing understanding in algebraic topology and homological algebra.

Contribution

It proves a new isomorphism relating topological cyclic homology and cyclic homology for DG categories over fields of characteristic p.

Findings

Isomorphism between p-adically completed topological cyclic homology and cyclic homology.

Applicable to DG categories over perfect fields of characteristic p.

Extends previous results to the setting of Witt vector liftings.

Abstract

We prove that the $p$-adically completed periodic topological cyclic homology of a DG category over a perfect field $k$ of characteristic $p>2$ is isomorphic to the ($p$-adically completed) periodic cyclic homology of a lifting of the DG category over the Witt vectors $W(k)$.