On quasi-categories of comodules and landweber exactness

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.