Monochromatic homotopy theory is asymptotically algebraic

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  • Tobias Barthel
  • Tomer M. Schlank
  • Nathaniel Stapleton

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.

OriginalsprogEngelsk
Artikelnummer107999
TidsskriftAdvances in Mathematics
Vol/bind393
ISSN0001-8708
DOI
StatusUdgivet - 2021

Bibliografisk 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 .

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© 2021

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