## 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 |
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Article number | 107999 |

Journal | Advances in Mathematics |

Volume | 393 |

DOIs | |

State | Published - Dec 24 2021 |

### Bibliographical note

Publisher Copyright:© 2021

### Funding

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 .

Funders | Funder number |
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Alon Fellowship | ISF 1588/18 |

National Science Foundation (NSF) | DMS-1906236 |

Horizon 2020 Framework Programme | |

H2020 Marie Skłodowska-Curie Actions | 751794 |

Engineering and Physical Sciences Research Council | EP/K032208/1 |

United States-Israel Binational Science Foundation | 2018389 |

Horizon 2020 |

## Keywords

- Ultraproduct chromatic homotopy theory

## ASJC Scopus subject areas

- General Mathematics