{"title":"Chow rings of quasi-split geometrically almost simple algebraic groups","authors":"Alexey Ananyevskiy, Nikita Geldhauser","doi":"arxiv-2408.09390","DOIUrl":null,"url":null,"abstract":"We compute the Chow ring of a quasi-split geometrically almost simple\nalgebraic group assuming the coefficients to be a field. This extends the\nclassical computation for split groups done by Kac to the non-split quasi-split\ncase. For the proof we introduce and study equivariant conormed Chow rings,\nwhich are well adapted to the study of quasi-split groups and their homogeneous\nvarieties.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - K-Theory and Homology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.09390","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
We compute the Chow ring of a quasi-split geometrically almost simple
algebraic group assuming the coefficients to be a field. This extends the
classical computation for split groups done by Kac to the non-split quasi-split
case. For the proof we introduce and study equivariant conormed Chow rings,
which are well adapted to the study of quasi-split groups and their homogeneous
varieties.