On quasi-categories of comodules and landweber exactness

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 Gn-spectra is a model of the K(n)-local category, where Gn is the extended Morava stabilizer group.

Original languageEnglish
Title of host publicationBousfield Classes and Ohkawa’s Theorem, BouCla 2015
EditorsTakeo Ohsawa, Norihiko Minami
PublisherSpringer
Pages325-380
Number of pages56
ISBN (Print)9789811515873
DOIs
Publication statusPublished - Jan 1 2020
EventInternational Conference on Bousfield Classes form a set: in Memory of Testusuke Ohkawa, BouCla 2015 - Nagoya, Japan
Duration: Aug 28 2015Aug 30 2015

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume309
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Conference on Bousfield Classes form a set: in Memory of Testusuke Ohkawa, BouCla 2015
CountryJapan
CityNagoya
Period8/28/158/30/15

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Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Torii, T. (2020). On quasi-categories of comodules and landweber exactness. In T. Ohsawa, & N. Minami (Eds.), 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