{"title":"On Weil–Stark elements, I: Construction and general properties","authors":"David Burns, Daniel Macias Castillo, Soogil Seo","doi":"10.1112/jlms.70001","DOIUrl":null,"url":null,"abstract":"<p>We construct a canonical family of elements in the reduced exterior powers of unit groups of global fields and investigate their detailed arithmetic properties. We then show that these elements specialise to recover the classical theory of cyclotomic elements in real abelian fields and also have connections to the theory of non-commutative Euler systems for <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>Z</mi>\n <mi>p</mi>\n </msub>\n <mrow>\n <mo>(</mo>\n <mn>1</mn>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$\\mathbb {Z}_p(1)$</annotation>\n </semantics></math> over general number fields.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70001","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/jlms.70001","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We construct a canonical family of elements in the reduced exterior powers of unit groups of global fields and investigate their detailed arithmetic properties. We then show that these elements specialise to recover the classical theory of cyclotomic elements in real abelian fields and also have connections to the theory of non-commutative Euler systems for over general number fields.
期刊介绍：
The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.
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