K-theory and topological cyclic homology of Henselian pairs

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K-theory and topological cyclic homology of Henselian pairs. / Clausen, Dustin; Mathew, Akhil; Morrow, Matthew.

In: Journal of the American Mathematical Society, Vol. 34, No. 2, 2021, p. 411-473.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Clausen, D, Mathew, A & Morrow, M 2021, 'K-theory and topological cyclic homology of Henselian pairs', Journal of the American Mathematical Society, vol. 34, no. 2, pp. 411-473. https://doi.org/10.1090/jams/961

APA

Clausen, D., Mathew, A., & Morrow, M. (2021). K-theory and topological cyclic homology of Henselian pairs. Journal of the American Mathematical Society, 34(2), 411-473. https://doi.org/10.1090/jams/961

Vancouver

Clausen D, Mathew A, Morrow M. K-theory and topological cyclic homology of Henselian pairs. Journal of the American Mathematical Society. 2021;34(2):411-473. https://doi.org/10.1090/jams/961

Author

Clausen, Dustin ; Mathew, Akhil ; Morrow, Matthew. / K-theory and topological cyclic homology of Henselian pairs. In: Journal of the American Mathematical Society. 2021 ; Vol. 34, No. 2. pp. 411-473.

Bibtex

@article{841d712c81874110a939ae7761fd63ac,
title = "K-theory and topological cyclic homology of Henselian pairs",
abstract = "Given a henselian pair (R,I) of commutative rings, we show that the relative K-theory and relative topological cyclic homology with finite coefficients are identified via the cyclotomic trace K→TC. This yields a generalization of the classical Gabber-Gillet-Thomason-Suslin rigidity theorem (for mod n coefficients, with n invertible in R) and McCarthy's theorem on relative K-theory (when I is nilpotent).We deduce that the cyclotomic trace is an equivalence in large degrees between p-adic K-theory and topological cyclic homology for a large class of p-adic rings. In addition, we show that K-theory with finite coefficients satisfies continuity for complete noetherian rings which are F-finite modulo p. Our main new ingredient is a basic finiteness property of TC with finite coefficients.",
author = "Dustin Clausen and Akhil Mathew and Matthew Morrow",
note = "Funding Information: We are grateful to Benjamin Antieau, Bhargav Bhatt, Lars Hesselholt, Thomas Nikolaus, and Peter Scholze for helpful discussions. We thank the referees for many helpful comments on an earlier version of the paper. The second author would like to thank the Universit? Paris 13, the Institut de Math?matiques de Jussieu-Paris Rive Gauche, and the University of Copenhagen for hospitality during which parts of this work were done.",
year = "2021",
doi = "10.1090/jams/961",
language = "English",
volume = "34",
pages = "411--473",
journal = "Journal of the American Mathematical Society",
issn = "0894-0347",
publisher = "American Mathematical Society",
number = "2",

}

RIS

TY - JOUR

T1 - K-theory and topological cyclic homology of Henselian pairs

AU - Clausen, Dustin

AU - Mathew, Akhil

AU - Morrow, Matthew

N1 - Funding Information: We are grateful to Benjamin Antieau, Bhargav Bhatt, Lars Hesselholt, Thomas Nikolaus, and Peter Scholze for helpful discussions. We thank the referees for many helpful comments on an earlier version of the paper. The second author would like to thank the Universit? Paris 13, the Institut de Math?matiques de Jussieu-Paris Rive Gauche, and the University of Copenhagen for hospitality during which parts of this work were done.

PY - 2021

Y1 - 2021

N2 - Given a henselian pair (R,I) of commutative rings, we show that the relative K-theory and relative topological cyclic homology with finite coefficients are identified via the cyclotomic trace K→TC. This yields a generalization of the classical Gabber-Gillet-Thomason-Suslin rigidity theorem (for mod n coefficients, with n invertible in R) and McCarthy's theorem on relative K-theory (when I is nilpotent).We deduce that the cyclotomic trace is an equivalence in large degrees between p-adic K-theory and topological cyclic homology for a large class of p-adic rings. In addition, we show that K-theory with finite coefficients satisfies continuity for complete noetherian rings which are F-finite modulo p. Our main new ingredient is a basic finiteness property of TC with finite coefficients.

AB - Given a henselian pair (R,I) of commutative rings, we show that the relative K-theory and relative topological cyclic homology with finite coefficients are identified via the cyclotomic trace K→TC. This yields a generalization of the classical Gabber-Gillet-Thomason-Suslin rigidity theorem (for mod n coefficients, with n invertible in R) and McCarthy's theorem on relative K-theory (when I is nilpotent).We deduce that the cyclotomic trace is an equivalence in large degrees between p-adic K-theory and topological cyclic homology for a large class of p-adic rings. In addition, we show that K-theory with finite coefficients satisfies continuity for complete noetherian rings which are F-finite modulo p. Our main new ingredient is a basic finiteness property of TC with finite coefficients.

UR - http://www.scopus.com/inward/record.url?scp=85104399212&partnerID=8YFLogxK

U2 - 10.1090/jams/961

DO - 10.1090/jams/961

M3 - Journal article

AN - SCOPUS:85104399212

VL - 34

SP - 411

EP - 473

JO - Journal of the American Mathematical Society

JF - Journal of the American Mathematical Society

SN - 0894-0347

IS - 2

ER -

ID: 301634265