{"title":"MORAVA K-THEORY AND FILTRATIONS BY POWERS","authors":"T. Barthel, Piotr Pstrągowski","doi":"10.1017/s1474748023000233","DOIUrl":null,"url":null,"abstract":"\n 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.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":" ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2021-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Institute of Mathematics of Jussieu","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s1474748023000233","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
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 stabiliser group. As an application, we compute the zeroth limit at all primes and heights.
期刊介绍：
The Journal of the Institute of Mathematics of Jussieu publishes original research papers in any branch of pure mathematics; papers in logic and applied mathematics will also be considered, particularly when they have direct connections with pure mathematics. Its policy is to feature a wide variety of research areas and it welcomes the submission of papers from all parts of the world. Selection for publication is on the basis of reports from specialist referees commissioned by the Editors.
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