Localizations of Morava E-theory and deformations of formal groups

Abstract

We study the relationship between the transchromatic localizations of Morava $E$-theory, $L_{K(n-1)}{E}_n$, and formal groups. In particular, we show that the coefficient ring ${\pi }_0{L}_{K(n-1)}{E}_n$ has a modular interpretation, representing deformations of formal groups with certain extra structure, and derive similar descriptions of the cooperations algebra and $E_{n-1}$-homology of this spectrum. As an application, we show that $L_{K(1)}{E}_2$ has exotic ${\mathcal{E}}_{\infty }$ structures not obtained by $K(1)$-localizing the ${\mathcal{E}}_{\infty }$ ring $E_2$.

32 pages, comments welcome. Corrected arguments in the proofs of Proposition 6.9 and Theorem 6.19

References in corpus (3)

• An introduction to higher dimensional local fields and adeles
• The Theory of Witt Vectors
• Towards solid abelian groups: A formal proof of Nöbeling's theorem