### Abstract

In this paper we study quasi-categories of comodules over coalgebras in a stable homotopy theory. We show that the quasi-category of comodules over the coalgebra associated to a Landweber exact S-algebra depends only on the height of the associated formal group. We also show that the quasi-category of E(n)-local spectra is equivalent to the quasi-category of comodules over the coalgebra (Formula Presented) for any Landweber exact S_{(p)}-algebra A of height n at a prime p. Furthermore, we show that the category of module objects over a discrete model of the Morava E-theory spectrum in K(n)-local discrete symmetric G_{n}-spectra is a model of the K(n)-local category, where G_{n} is the extended Morava stabilizer group.

Original language | English |
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Title of host publication | Bousfield Classes and Ohkawa’s Theorem, BouCla 2015 |

Editors | Takeo Ohsawa, Norihiko Minami |

Publisher | Springer |

Pages | 325-380 |

Number of pages | 56 |

ISBN (Print) | 9789811515873 |

DOIs | |

Publication status | Published - Jan 1 2020 |

Event | International Conference on Bousfield Classes form a set: in Memory of Testusuke Ohkawa, BouCla 2015 - Nagoya, Japan Duration: Aug 28 2015 → Aug 30 2015 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 309 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Conference

Conference | International Conference on Bousfield Classes form a set: in Memory of Testusuke Ohkawa, BouCla 2015 |
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Country | Japan |

City | Nagoya |

Period | 8/28/15 → 8/30/15 |

### Fingerprint

### Keywords

- Comodule
- Complex oriented spectrum
- K(n)-local category
- Landweber exactness
- Quasi-Category
- Stable homotopy theroy

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Bousfield Classes and Ohkawa’s Theorem, BouCla 2015*(pp. 325-380). (Springer Proceedings in Mathematics and Statistics; Vol. 309). Springer. https://doi.org/10.1007/978-981-15-1588-0_11