THH 上的五月过滤和忠实的平缓下降

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra Pub Date : 2024-09-26 DOI:10.1016/j.jpaa.2024.107806

Liam Keenan

{"title":"THH 上的五月过滤和忠实的平缓下降","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":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"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}","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

摘要

在本文中，我们研究了拓扑霍赫希尔德同调和拓扑循环同调的下降性质。特别是，我们验证了这两个不变式都满足连通 E2 环谱的忠实平坦下降和 1-connective 下降。这分别推广了[6]中 Bhatt-Morrow-Scholze 的一个结果和[11]中 Dundas-Rognes 的一个结果。在此过程中，我们发展了一些关于科巴构造的基本理论，并给出了拓扑霍赫希尔德同调的梅滤波的另一种表述，该表述最初是由 Angelini-Knoll-Salch [3] 提出的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

The May filtration on THH and faithfully flat descent

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

E_{2}

-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].

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Pure and Applied Algebra 数学-数学

CiteScore

1.70

自引率

12.50%

发文量

225

审稿时长

17 days

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.