Uniqueness of Morava K-theory

Abstract

We show that there is an essentially unique S-algebra structure on the Morava K-theory spectrum K(n), while K(n) has uncountably many MU or \hE{n}-algebra structures. Here \hE{n} is the K(n)-localized Johnson-Wilson spectrum. To prove this we set up a spectral sequence computing the homotopy groups of the moduli space of A-infinity structures on a spectrum, and use the theory of S-algebra k-invariants for connective S-algebras due to Dugger and Shipley to show that all the uniqueness obstructions are hit by differentials.

16 pages. Minor modifications, to appear in Compositio Mathematica.

References in corpus (2)

• Topological Hochschild homology and cohomology of A_\infty ring spectra
• Postnikov extensions of ring spectra

Cited by in corpus (7)

• The tangent complex and Hochschild cohomology of E_n-rings
• Twisted Morava K-theory and E-theory
• Algebraic K-theory of strict ring spectra
• Algebraic K-theory of the fraction field of topological K-theory
• Enhanced $A$-infinity obstruction theory
• Morava K-theory and Filtrations by Powers
• Gross-Hopkins duality and the Gorenstein condition