Remarks on K(1)-local K-theory

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

Standard

Remarks on K(1)-local K-theory. / Bhatt, Bhargav; Clausen, Dustin; Mathew, Akhil.

In: Selecta Mathematica, Vol. 26, No. 3, 39, 2020.

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

Harvard

Bhatt, B, Clausen, D & Mathew, A 2020, 'Remarks on K(1)-local K-theory', Selecta Mathematica, vol. 26, no. 3, 39. https://doi.org/10.1007/s00029-020-00566-6

APA

Bhatt, B., Clausen, D., & Mathew, A. (2020). Remarks on K(1)-local K-theory. Selecta Mathematica, 26(3), [39]. https://doi.org/10.1007/s00029-020-00566-6

Vancouver

Bhatt B, Clausen D, Mathew A. Remarks on K(1)-local K-theory. Selecta Mathematica. 2020;26(3). 39. https://doi.org/10.1007/s00029-020-00566-6

Author

Bhatt, Bhargav ; Clausen, Dustin ; Mathew, Akhil. / Remarks on K(1)-local K-theory. In: Selecta Mathematica. 2020 ; Vol. 26, No. 3.

Bibtex

@article{757e78420d0540518cd7e382a9304519,
title = "Remarks on K(1)-local K-theory",
abstract = "We prove two basic structural properties of the algebraic K-theory of rings after K(1)-localization at an implicit prime p. Our first result (also recently obtained by Land–Meier–Tamme by different methods) states that LK(1)K(R) is insensitive to inverting p on R; we deduce this from recent advances in prismatic cohomology and TC. Our second result yields a K{\"u}nneth formula in K(1)-local K-theory for adding p-power roots of unity to R. ",
author = "Bhargav Bhatt and Dustin Clausen and Akhil Mathew",
year = "2020",
doi = "10.1007/s00029-020-00566-6",
language = "English",
volume = "26",
journal = "Selecta Mathematica, New Series",
issn = "1022-1824",
publisher = "Springer",
number = "3",

}

RIS

TY - JOUR

T1 - Remarks on K(1)-local K-theory

AU - Bhatt, Bhargav

AU - Clausen, Dustin

AU - Mathew, Akhil

PY - 2020

Y1 - 2020

N2 - We prove two basic structural properties of the algebraic K-theory of rings after K(1)-localization at an implicit prime p. Our first result (also recently obtained by Land–Meier–Tamme by different methods) states that LK(1)K(R) is insensitive to inverting p on R; we deduce this from recent advances in prismatic cohomology and TC. Our second result yields a Künneth formula in K(1)-local K-theory for adding p-power roots of unity to R.

AB - We prove two basic structural properties of the algebraic K-theory of rings after K(1)-localization at an implicit prime p. Our first result (also recently obtained by Land–Meier–Tamme by different methods) states that LK(1)K(R) is insensitive to inverting p on R; we deduce this from recent advances in prismatic cohomology and TC. Our second result yields a Künneth formula in K(1)-local K-theory for adding p-power roots of unity to R.

U2 - 10.1007/s00029-020-00566-6

DO - 10.1007/s00029-020-00566-6

M3 - Journal article

VL - 26

JO - Selecta Mathematica, New Series

JF - Selecta Mathematica, New Series

SN - 1022-1824

IS - 3

M1 - 39

ER -

ID: 259823810