Topological cyclic homology
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Topological cyclic homology. / Hesselholt, Lars; Nikolaus, Thomas.
Handbook of Homotopy Theory. red. / Haynes Miller. 1. udg. CRC Press, 2019. (CRC Press/Chapman and Hall Handbooks in Mathematics Series).Publikation: Bidrag til bog/antologi/rapport › Bidrag til bog/antologi › Forskning
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TY - CHAP
T1 - Topological cyclic homology
AU - Hesselholt, Lars
AU - Nikolaus, Thomas
PY - 2019
Y1 - 2019
N2 - 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 It contains a proof of the Bökstedt periodicity theorem close to his original unpublished proof, as well as the proof by Bhatt-Morrow-Scholze of its extension to all perfectoid rings.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.
AB - 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 It contains a proof of the Bökstedt periodicity theorem close to his original unpublished proof, as well as the proof by Bhatt-Morrow-Scholze of its extension to all perfectoid rings.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.
UR - https://www.crcpress.com/Handbook-of-Homotopy-Theory/Miller/p/book/9780815369707
M3 - Book chapter
SN - 9780815369707
T3 - CRC Press/Chapman and Hall Handbooks in Mathematics Series
BT - Handbook of Homotopy Theory
A2 - Miller, Haynes
PB - CRC Press
ER -
ID: 231710326