{"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":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Israel Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11856-023-2593-6","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
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.
期刊介绍：
The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.
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