Morava K-theory and Filtrations by Powers

2021/11/11 by Tobias Barthel, Piotr Pstrągowski, Barthel, Tobias +1
Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2111.06379

openalex publication_date 2021/11/11 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

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 stabilizer group. As an application, we compute the zeroth limit at all primes and heights.

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