{"title":"关于ε因子的微局部几何局部化公式","authors":"Tomoyuki Abe, D. Patel","doi":"10.2140/AKT.2018.3.461","DOIUrl":null,"url":null,"abstract":"Given a lisse l-adic sheaf G on a smooth proper variety X and a lisse sheaf F on an open dense U in X, Kato and Saito conjectured a localization formula for the global l-adic epsilon factor εl(X,F ⊗ G) in terms of the global epsilon factor of F and a certain intersection number associated to det(G) and the Swan class of F . In this article, we prove an analog of this conjecture for global de Rham epsilon factors in the classical setting of DX -modules on smooth projective varieties over a field of characteristic zero.","PeriodicalId":42182,"journal":{"name":"Annals of K-Theory","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2018-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/AKT.2018.3.461","citationCount":"6","resultStr":"{\"title\":\"On a localization formula of epsilon factors via microlocal geometry\",\"authors\":\"Tomoyuki Abe, D. Patel\",\"doi\":\"10.2140/AKT.2018.3.461\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given a lisse l-adic sheaf G on a smooth proper variety X and a lisse sheaf F on an open dense U in X, Kato and Saito conjectured a localization formula for the global l-adic epsilon factor εl(X,F ⊗ G) in terms of the global epsilon factor of F and a certain intersection number associated to det(G) and the Swan class of F . In this article, we prove an analog of this conjecture for global de Rham epsilon factors in the classical setting of DX -modules on smooth projective varieties over a field of characteristic zero.\",\"PeriodicalId\":42182,\"journal\":{\"name\":\"Annals of K-Theory\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2018-07-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.2140/AKT.2018.3.461\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of K-Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/AKT.2018.3.461\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of K-Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/AKT.2018.3.461","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On a localization formula of epsilon factors via microlocal geometry
Given a lisse l-adic sheaf G on a smooth proper variety X and a lisse sheaf F on an open dense U in X, Kato and Saito conjectured a localization formula for the global l-adic epsilon factor εl(X,F ⊗ G) in terms of the global epsilon factor of F and a certain intersection number associated to det(G) and the Swan class of F . In this article, we prove an analog of this conjecture for global de Rham epsilon factors in the classical setting of DX -modules on smooth projective varieties over a field of characteristic zero.
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