{"title":"Local Langlands correspondences in $$\\ell $$ -adic coefficients","authors":"Naoki Imai","doi":"10.1007/s00229-024-01582-y","DOIUrl":null,"url":null,"abstract":"<p>Let <span>\\(\\ell \\)</span> be a prime number different from the residue characteristic of a non-archimedean local field <i>F</i>. We give formulations of <span>\\(\\ell \\)</span>-adic local Langlands correspondences for connected reductive algebraic groups over <i>F</i>, which we conjecture to be independent of a choice of an isomorphism between the <span>\\(\\ell \\)</span>-adic coefficient field and the complex number field.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-21","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/s00229-024-01582-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let \(\ell \) be a prime number different from the residue characteristic of a non-archimedean local field F. We give formulations of \(\ell \)-adic local Langlands correspondences for connected reductive algebraic groups over F, which we conjecture to be independent of a choice of an isomorphism between the \(\ell \)-adic coefficient field and the complex number field.