Topological cyclic homology

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearch

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 It contains a proof of the Bökstedt periodicity theorem close to his original unpublished proof, as well as the proof by Bhatt-Morrow-Scholze of its extension to all perfectoid rings.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.
Original languageEnglish
Title of host publicationHandbook of Homotopy Theory
EditorsHaynes Miller
PublisherCRC Press
Publication date2019
Edition1
Chapter15
ISBN (Print)9780815369707
Publication statusPublished - 2019
SeriesCRC Press/Chapman and Hall Handbooks in Mathematics Series

ID: 231710326