Topological cyclic homology
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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 It contains a proof of the Bökstedt periodicity theorem close to his original unpublished proof, as well as the proof by Bhatt-Morrow-Scholze of its extension to all perfectoid rings.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 language | English |
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Title of host publication | Handbook of Homotopy Theory |
Editors | Haynes Miller |
Publisher | CRC Press |
Publication date | 2019 |
Edition | 1 |
Chapter | 15 |
ISBN (Print) | 9780815369707 |
Publication status | Published - 2019 |
Series | CRC Press/Chapman and Hall Handbooks in Mathematics Series |
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ID: 231710326