{"title":"Global algebraic K-theory","authors":"Stefan Schwede","doi":"10.1112/topo.12241","DOIUrl":null,"url":null,"abstract":"<p>We introduce a global equivariant refinement of algebraic K-theory; here ‘global equivariant’ refers to simultaneous and compatible actions of all finite groups. Our construction turns a specific kind of categorical input data into a global <math>\n <semantics>\n <mi>Ω</mi>\n <annotation>$\\Omega$</annotation>\n </semantics></math>-spectrum that keeps track of genuine <math>\n <semantics>\n <mi>G</mi>\n <annotation>$G$</annotation>\n </semantics></math>-equivariant infinite loop spaces, for all finite groups <math>\n <semantics>\n <mi>G</mi>\n <annotation>$G$</annotation>\n </semantics></math>. The resulting global algebraic K-theory spectrum is a rigid way of packaging the representation K-theory, or ‘Swan K-theory’ into one highly structured object.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2022-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12241","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12241","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: 8
Abstract
We introduce a global equivariant refinement of algebraic K-theory; here ‘global equivariant’ refers to simultaneous and compatible actions of all finite groups. Our construction turns a specific kind of categorical input data into a global -spectrum that keeps track of genuine -equivariant infinite loop spaces, for all finite groups . The resulting global algebraic K-theory spectrum is a rigid way of packaging the representation K-theory, or ‘Swan K-theory’ into one highly structured object.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
