Monochromatic homotopy theory is asymptotically algebraic

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Standard

Monochromatic homotopy theory is asymptotically algebraic. / Barthel, Tobias; Schlank, Tomer M.; Stapleton, Nathaniel.

I: Advances in Mathematics, Bind 393, 107999, 2021.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Barthel, T, Schlank, TM & Stapleton, N 2021, 'Monochromatic homotopy theory is asymptotically algebraic', Advances in Mathematics, bind 393, 107999. https://doi.org/10.1016/j.aim.2021.107999

APA

Barthel, T., Schlank, T. M., & Stapleton, N. (2021). Monochromatic homotopy theory is asymptotically algebraic. Advances in Mathematics, 393, [107999]. https://doi.org/10.1016/j.aim.2021.107999

Vancouver

Barthel T, Schlank TM, Stapleton N. Monochromatic homotopy theory is asymptotically algebraic. Advances in Mathematics. 2021;393. 107999. https://doi.org/10.1016/j.aim.2021.107999

Author

Barthel, Tobias ; Schlank, Tomer M. ; Stapleton, Nathaniel. / Monochromatic homotopy theory is asymptotically algebraic. I: Advances in Mathematics. 2021 ; Bind 393.

Bibtex

@article{00cb21a08ef34727bc8d8015d30cba86,
title = "Monochromatic homotopy theory is asymptotically algebraic",
abstract = "In previous work, we used an ∞-categorical version of ultraproducts to show that, for a fixed height n, the symmetric monoidal ∞-categories of En,p-local spectra are asymptotically algebraic in the prime p. In this paper, we prove the analogous result for the symmetric monoidal ∞-categories of Kp(n)-local spectra, where Kp(n) is Morava K-theory at height n and the prime p. This requires ∞-categorical tools suitable for working with compactly generated symmetric monoidal ∞-categories with non-compact unit. The equivalences that we produce here are compatible with the equivalences for the En,p-local ∞-categories.",
keywords = "Ultraproduct chromatic homotopy theory",
author = "Tobias Barthel and Schlank, {Tomer M.} and Nathaniel Stapleton",
note = "Publisher Copyright: {\textcopyright} 2021",
year = "2021",
doi = "10.1016/j.aim.2021.107999",
language = "English",
volume = "393",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Monochromatic homotopy theory is asymptotically algebraic

AU - Barthel, Tobias

AU - Schlank, Tomer M.

AU - Stapleton, Nathaniel

N1 - Publisher Copyright: © 2021

PY - 2021

Y1 - 2021

N2 - In previous work, we used an ∞-categorical version of ultraproducts to show that, for a fixed height n, the symmetric monoidal ∞-categories of En,p-local spectra are asymptotically algebraic in the prime p. In this paper, we prove the analogous result for the symmetric monoidal ∞-categories of Kp(n)-local spectra, where Kp(n) is Morava K-theory at height n and the prime p. This requires ∞-categorical tools suitable for working with compactly generated symmetric monoidal ∞-categories with non-compact unit. The equivalences that we produce here are compatible with the equivalences for the En,p-local ∞-categories.

AB - In previous work, we used an ∞-categorical version of ultraproducts to show that, for a fixed height n, the symmetric monoidal ∞-categories of En,p-local spectra are asymptotically algebraic in the prime p. In this paper, we prove the analogous result for the symmetric monoidal ∞-categories of Kp(n)-local spectra, where Kp(n) is Morava K-theory at height n and the prime p. This requires ∞-categorical tools suitable for working with compactly generated symmetric monoidal ∞-categories with non-compact unit. The equivalences that we produce here are compatible with the equivalences for the En,p-local ∞-categories.

KW - Ultraproduct chromatic homotopy theory

U2 - 10.1016/j.aim.2021.107999

DO - 10.1016/j.aim.2021.107999

M3 - Journal article

AN - SCOPUS:85116697365

VL - 393

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

M1 - 107999

ER -

ID: 306971575