{"title":"On a conjecture of Braverman-Kazhdan","authors":"Tsao-Hsien Chen","doi":"10.1090/jams/992","DOIUrl":null,"url":null,"abstract":"Abstract:In this article we prove a conjecture of Braverman-Kazhdan in [Geom. Funct. Anal. Special Volume (2000), pp. 237–278] on acyclicity of $\\rho$-Bessel sheaves on reductive groups. We do so by proving a vanishing conjecture proposed in our previous work [A vanishing conjecture: the GLn case, arXiv:1902.11190]. As a corollary, we obtain a geometric construction of the non-linear Fourier kernel for a finite reductive group as conjectured by Braverman and Kazhdan. The proof uses the theory of Mellin transforms, Drinfeld center of Harish-Chandra bimodules, and a construction of a class of character sheaves in mixed-characteristic. <hr align=\"left\" noshade=\"noshade\" width=\"200\"/>","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":"47 1","pages":""},"PeriodicalIF":3.5000,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the American Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/jams/992","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract:In this article we prove a conjecture of Braverman-Kazhdan in [Geom. Funct. Anal. Special Volume (2000), pp. 237–278] on acyclicity of $\rho$-Bessel sheaves on reductive groups. We do so by proving a vanishing conjecture proposed in our previous work [A vanishing conjecture: the GLn case, arXiv:1902.11190]. As a corollary, we obtain a geometric construction of the non-linear Fourier kernel for a finite reductive group as conjectured by Braverman and Kazhdan. The proof uses the theory of Mellin transforms, Drinfeld center of Harish-Chandra bimodules, and a construction of a class of character sheaves in mixed-characteristic.
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