Morava K理论的唯一性
Uniqueness of Morava K-theory
摘要：
我们证明了Morava K-理论谱K（n）上存在一个本质上唯一的S-代数结构，而K（n）上有无数个MU或\hE{n} -代数结构.这里\hE{n}是K（n）定域的约翰逊-威尔逊谱。为了证明这一点，我们建立了一个谱序列来计算谱上A-无限结构的模空间的同伦群，并利用Dugger和Shipley关于连通S-代数的S-代数k-不变量理论证明了所有的唯一性障碍都被微分击中.
英文摘要：
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.
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