{"title":"通过 K 理论的博克斯特周期性发生器","authors":"Anton Fonarev, Dmitry Kaledin","doi":"10.1007/s11856-023-2593-6","DOIUrl":null,"url":null,"abstract":"<p>For a prime field <i>k</i> of characteristic <i>p</i> > 2, we construct the Bökstedt periodicity generator <i>v</i> ∈ <i>THH</i><sub>2</sub>(<i>k</i>) as an explicit class in the stabilization of K-theory with coefficients <i>K</i>(<i>k</i>, −), and we show directly that <i>v</i> is not nilpotent in <i>THH</i>(<i>k</i>). This gives an alternative proof of the “multiplicative” part of Bökstedt periodicity.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bökstedt periodicity generator via K-theory\",\"authors\":\"Anton Fonarev, Dmitry Kaledin\",\"doi\":\"10.1007/s11856-023-2593-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>For a prime field <i>k</i> of characteristic <i>p</i> > 2, we construct the Bökstedt periodicity generator <i>v</i> ∈ <i>THH</i><sub>2</sub>(<i>k</i>) as an explicit class in the stabilization of K-theory with coefficients <i>K</i>(<i>k</i>, −), and we show directly that <i>v</i> is not nilpotent in <i>THH</i>(<i>k</i>). This gives an alternative proof of the “multiplicative” part of Bökstedt periodicity.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-12-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11856-023-2593-6\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11856-023-2593-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
对于特性为 p > 2 的素域 k，我们在 K 理论的稳定化中以系数 K(k, -) 作为显式类构造了博克斯特德周期性生成器 v∈THH2(k) ，并直接证明了 v 在 THH(k) 中并非零势。这为博克斯特周期性的 "乘法 "部分提供了另一种证明。
For a prime field k of characteristic p > 2, we construct the Bökstedt periodicity generator v ∈ THH2(k) as an explicit class in the stabilization of K-theory with coefficients K(k, −), and we show directly that v is not nilpotent in THH(k). This gives an alternative proof of the “multiplicative” part of Bökstedt periodicity.
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