{"title":"The May filtration on THH and faithfully flat descent","authors":"Liam Keenan","doi":"10.1016/j.jpaa.2024.107806","DOIUrl":null,"url":null,"abstract":"<div><div>In this article, we study descent properties of topological Hochschild homology and topological cyclic homology. In particular, we verify that both of these invariants satisfy faithfully flat descent and 1-connective descent for connective <span><math><msub><mrow><mi>E</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-ring spectra. This generalizes a result of Bhatt–Morrow–Scholze from <span><span>[6]</span></span> and a result of Dundas–Rognes from <span><span>[11]</span></span>, respectively. Along the way, we develop some basic theory for cobar constructions and give an alternative presentation of the May filtration on topological Hochschild homology, originally due to Angelini-Knoll–Salch <span><span>[3]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107806"},"PeriodicalIF":0.8000,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pure and Applied Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022404924002032","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we study descent properties of topological Hochschild homology and topological cyclic homology. In particular, we verify that both of these invariants satisfy faithfully flat descent and 1-connective descent for connective -ring spectra. This generalizes a result of Bhatt–Morrow–Scholze from [6] and a result of Dundas–Rognes from [11], respectively. Along the way, we develop some basic theory for cobar constructions and give an alternative presentation of the May filtration on topological Hochschild homology, originally due to Angelini-Knoll–Salch [3].
期刊介绍：
The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.
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