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 \(\mathbb {S}\)-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 \(A\otimes A\) for any Landweber exact \(\mathbb {S}_{(p)}\)-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 \(\mathbb {G}_n\)-spectra is a model of the K(n)-local category, where \(\mathbb {G}_n\) is the extended Morava stabilizer group.
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The author would like to thank the anonymous referee for careful reading of the manuscript and helpful comments.
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Torii, T. (2020). On Quasi-Categories of Comodules and Landweber Exactness. In: Ohsawa, T., Minami, N. (eds) Bousfield Classes and Ohkawa's Theorem. BouCla 2015. Springer Proceedings in Mathematics & Statistics, vol 309. Springer, Singapore. https://doi.org/10.1007/978-981-15-1588-0_11
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DOI: https://doi.org/10.1007/978-981-15-1588-0_11
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