We prove the convergence of the Adams spectral sequence based on Morava K-theory and relate it to the filtration by powers of the maximal ideal in the Lubin–Tate ring through a Miller square. We use the filtration by powers to construct a spectral sequence relating the homology of the K-local sphere to derived functors of completion and express the latter as cohomology of the Morava stabiliser group. As an application, we compute the zeroth limit at all primes and heights.

中文翻译：

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MORAVA K 理论和权力过滤

我们证明了基于Morava的Adams谱序列的收敛性K-理论并将其与鲁宾-泰特环中最大理想幂通过米勒平方的过滤联系起来。我们使用幂过滤来构建与同源性相关的谱序列K-局部球面到完成的派生函子并将后者表示为 Morava 稳定群的上同调。作为一个应用程序，我们计算所有素数和高度的零极限。