Monochromatic homotopy theory is asymptotically algebraic

Tobias Barthel; Tomer M. Schlank; Nathaniel Stapleton

doi:10.1016/j.aim.2021.107999

Monochromatic homotopy theory is asymptotically algebraic

Tobias Barthel, Tomer M. Schlank, Nathaniel Stapleton

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In previous work, we used an ∞-categorical version of ultraproducts to show that, for a fixed height n, the symmetric monoidal ∞-categories of E_n,p-local spectra are asymptotically algebraic in the prime p. In this paper, we prove the analogous result for the symmetric monoidal ∞-categories of K_p(n)-local spectra, where K_p(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 E_n,p-local ∞-categories.

Original language	English
Article number	107999
Journal	Advances in Mathematics
Volume	393
DOIs	https://doi.org/10.1016/j.aim.2021.107999
State	Published - Dec 24 2021

Bibliographical note

Funding Information:
The first author was partially supported by the DNRF92 and the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 751794 . The second author is supported by the Alon Fellowship and ISF 1588/18 . The third author is partially supported by NSF grant DMS-1906236 . The second and third authors are supported by BSF grant 2018389 . All three authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Homotopy Harnessing Higher Structures, where work on this paper was undertaken. This work was supported by EPSRC grant no. EP/K032208/1 .

Publisher Copyright:
© 2021

Keywords

Ultraproduct chromatic homotopy theory

ASJC Scopus subject areas

Mathematics (all)

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10.1016/j.aim.2021.107999

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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.",

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AU - Stapleton, Nathaniel

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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.

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Monochromatic homotopy theory is asymptotically algebraic

Abstract

Bibliographical note

Keywords

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