{"title":"A Remark on a Result of Huber and Kahn","authors":"Somayeh Habibi, Farhad Rahmati","doi":"10.1007/s41980-024-00861-4","DOIUrl":null,"url":null,"abstract":"<p>A. Huber and B. Kahn construct a relative slice filtration on the motive <i>M</i>(<i>X</i>) associated to a principal <i>T</i>-bundle <span>\\(X\\rightarrow Y\\)</span> for a smooth scheme <i>Y</i>. As a consequence of their result, one can observe that the mixed Tateness of the motive <i>M</i>(<i>Y</i>) implies that the motive <i>M</i>(<i>X</i>) is mixed Tate. In this note we prove the inverse implication for a principal <i>G</i>-bundle, for a split reductive group <i>G</i>.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Iranian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s41980-024-00861-4","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
A. Huber and B. Kahn construct a relative slice filtration on the motive M(X) associated to a principal T-bundle \(X\rightarrow Y\) for a smooth scheme Y. As a consequence of their result, one can observe that the mixed Tateness of the motive M(Y) implies that the motive M(X) is mixed Tate. In this note we prove the inverse implication for a principal G-bundle, for a split reductive group G.
期刊介绍：
The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.
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