Uniqueness of Morava K-theory

作者：Angeltveit Vigleik^*

来源：Compositio Mathematica, 2011, 147(2): 633-648.

DOI：10.1112/S0010437X10005026

• S-algebra
• Morava K-theory
• moduli space

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 <(E(n))over cap>-algebra structures. Here <(E(n))over cap> 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 found in the work of Dugger and Shipley [Postnikov extensions of ring spectra, Algebr. Geom. Topol. 6 (2006), 1785-1829 (electronic)] to show that all the uniqueness obstructions are hit by differentials.

• 出版日期2011-3