Topological cyclic homology

Publikation: Bidrag til bog/antologi/rapport › Bidrag til bog/antologi › Forskning

Standard

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

Harvard

Hesselholt, L & Nikolaus, T 2019, Topological cyclic homology. i H Miller (red.), Handbook of Homotopy Theory. 1 udg, CRC Press, CRC Press/Chapman and Hall Handbooks in Mathematics Series.

APA

Hesselholt, L., & Nikolaus, T. (2019). Topological cyclic homology. I H. Miller (red.), Handbook of Homotopy Theory (1 udg.). CRC Press. CRC Press/Chapman and Hall Handbooks in Mathematics Series

Vancouver

Hesselholt L, Nikolaus T. Topological cyclic homology. I Miller H, red., Handbook of Homotopy Theory. 1 udg. CRC Press. 2019. (CRC Press/Chapman and Hall Handbooks in Mathematics Series).

Author

Hesselholt, Lars ; Nikolaus, Thomas. / Topological cyclic homology. Handbook of Homotopy Theory. red. / Haynes Miller. 1. udg. CRC Press, 2019. (CRC Press/Chapman and Hall Handbooks in Mathematics Series).

Bibtex

@inbook{ce7b0617540e4886993ef3a498f30aee,
title = "Topological cyclic homology",
abstract = "This handbook chapter gives an introduction to topological cyclic homology following the modern setup of Nikolaus-Scholze. It contains a proof of the B{\"o}kstedt periodicity theorem close to his original unpublished proof, as well as the proof by Bhatt-Morrow-Scholze of its extension to all perfectoid rings.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.",
author = "Lars Hesselholt and Thomas Nikolaus",
year = "2019",
language = "English",
isbn = "9780815369707",
series = "CRC Press/Chapman and Hall Handbooks in Mathematics Series",
publisher = "CRC Press",
editor = "Haynes Miller",
booktitle = "Handbook of Homotopy Theory",
edition = "1",

}

RIS

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 It contains a proof of the Bökstedt periodicity theorem close to his original unpublished proof, as well as the proof by Bhatt-Morrow-Scholze of its extension to all perfectoid rings.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