{"title":"Correspondences and stable homotopy theory","authors":"Grigory Garkusha","doi":"10.1112/tlm3.12056","DOIUrl":null,"url":null,"abstract":"Abstract A general method of producing correspondences and spectral categories out of symmetric ring objects in general categories is given. As an application, stable homotopy theory of spectra is recovered from modules over a commutative symmetric ring spectrum defined in terms of framed correspondences over an algebraically closed field. Another application recovers stable motivic homotopy theory from spectral modules over associated spectral categories.","PeriodicalId":41208,"journal":{"name":"Transactions of the London Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the London Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1112/tlm3.12056","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract A general method of producing correspondences and spectral categories out of symmetric ring objects in general categories is given. As an application, stable homotopy theory of spectra is recovered from modules over a commutative symmetric ring spectrum defined in terms of framed correspondences over an algebraically closed field. Another application recovers stable motivic homotopy theory from spectral modules over associated spectral categories.
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