On quasi-categories of comodules and Landweber exactness

2016/12/10 by Torii, Takeshi
#55P42 #55P43 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.03265

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 A⊗ A 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 the 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.

Related

• Comodules and Landweber exact homology theories
• Comodule categories and the geometry of the stack of formal groups
• Comodules and contramodules over coalgebras associated with locally finite categories
• Witt, GW, K-theory of quasi-projective schemes
• Coalgebras in the Dwyer-Kan localization of a model category