Topological cyclic homology

This handbook chapter gives an introduction to topological cyclic homology following the modern setup of Nikolaus-Scholze. It contains a proof of the Bökstedt periodicity theorem close to his original unpublished proof, as well as the proof by Bhatt-Morrow-Scholze of its extension to all perfectoid rings. The latter is used to give a purely p-adic proof of the Bott periodicity theorem. Finally, the cofiber of the assembly map in p-adic K-theory for a cyclic group of order p and a perfectoid ring of coefficients is calculated.

Lars Hesselholt <>