{"title":"关于motivic-Segal猜想","authors":"Thomas Gregersen, John Rognes","doi":"10.1112/topo.12311","DOIUrl":null,"url":null,"abstract":"<p>We establish motivic versions of the theorems of Lin and Gunawardena, thereby confirming the motivic Segal conjecture for the algebraic group <math>\n <semantics>\n <msub>\n <mi>μ</mi>\n <mi>ℓ</mi>\n </msub>\n <annotation>$\\mu _\\ell$</annotation>\n </semantics></math> of <math>\n <semantics>\n <mi>ℓ</mi>\n <annotation>$\\ell$</annotation>\n </semantics></math>th roots of unity, where <math>\n <semantics>\n <mi>ℓ</mi>\n <annotation>$\\ell$</annotation>\n </semantics></math> is any prime. To achieve this we develop motivic Singer constructions associated to the symmetric group <math>\n <semantics>\n <msub>\n <mi>S</mi>\n <mi>ℓ</mi>\n </msub>\n <annotation>$S_\\ell$</annotation>\n </semantics></math> and to <math>\n <semantics>\n <msub>\n <mi>μ</mi>\n <mi>ℓ</mi>\n </msub>\n <annotation>$\\mu _\\ell$</annotation>\n </semantics></math>, and introduce a delayed limit Adams spectral sequence.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 3","pages":"1258-1313"},"PeriodicalIF":0.8000,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12311","citationCount":"1","resultStr":"{\"title\":\"On the motivic Segal conjecture\",\"authors\":\"Thomas Gregersen, John Rognes\",\"doi\":\"10.1112/topo.12311\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We establish motivic versions of the theorems of Lin and Gunawardena, thereby confirming the motivic Segal conjecture for the algebraic group <math>\\n <semantics>\\n <msub>\\n <mi>μ</mi>\\n <mi>ℓ</mi>\\n </msub>\\n <annotation>$\\\\mu _\\\\ell$</annotation>\\n </semantics></math> of <math>\\n <semantics>\\n <mi>ℓ</mi>\\n <annotation>$\\\\ell$</annotation>\\n </semantics></math>th roots of unity, where <math>\\n <semantics>\\n <mi>ℓ</mi>\\n <annotation>$\\\\ell$</annotation>\\n </semantics></math> is any prime. To achieve this we develop motivic Singer constructions associated to the symmetric group <math>\\n <semantics>\\n <msub>\\n <mi>S</mi>\\n <mi>ℓ</mi>\\n </msub>\\n <annotation>$S_\\\\ell$</annotation>\\n </semantics></math> and to <math>\\n <semantics>\\n <msub>\\n <mi>μ</mi>\\n <mi>ℓ</mi>\\n </msub>\\n <annotation>$\\\\mu _\\\\ell$</annotation>\\n </semantics></math>, and introduce a delayed limit Adams spectral sequence.</p>\",\"PeriodicalId\":56114,\"journal\":{\"name\":\"Journal of Topology\",\"volume\":\"16 3\",\"pages\":\"1258-1313\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12311\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Topology\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/topo.12311\",\"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 Topology","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12311","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: 1
摘要
我们建立了Lin定理和Gunawardena定理的动机版本，从而证实了对于单位n根的代数群μ r $\mu _\ell$的动机Segal猜想，其中，r $\ell$是任意素数。为此，我们建立了对称群S $S_\ell$和μ $S_\ell$的动机Singer结构，并引入了延迟极限Adams谱序列。
We establish motivic versions of the theorems of Lin and Gunawardena, thereby confirming the motivic Segal conjecture for the algebraic group of th roots of unity, where is any prime. To achieve this we develop motivic Singer constructions associated to the symmetric group and to , and introduce a delayed limit Adams spectral sequence.
期刊介绍：
The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal.
The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.
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