{"title":"La réalisation étale et les opérations de Grothendieck","authors":"J. Ayoub","doi":"10.24033/ASENS.2210","DOIUrl":null,"url":null,"abstract":"In this article, we construct etale realization functors defined on the categories DAet(X, Λ) of etale motives (without transfers) over a scheme X. Our construction is natural and relies on a relative rigidity theorem a la Suslin-Voevodsky that we will establish first. Then, we show that these realization functors are compatible with Grothendieck operations and the \"nearby cycles\" functors. Along the way, we prove a number of properties concerning etale motives.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"7 1","pages":"1-145"},"PeriodicalIF":1.3000,"publicationDate":"2014-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"109","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Scientifiques De L Ecole Normale Superieure","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.24033/ASENS.2210","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: 109
Abstract
In this article, we construct etale realization functors defined on the categories DAet(X, Λ) of etale motives (without transfers) over a scheme X. Our construction is natural and relies on a relative rigidity theorem a la Suslin-Voevodsky that we will establish first. Then, we show that these realization functors are compatible with Grothendieck operations and the "nearby cycles" functors. Along the way, we prove a number of properties concerning etale motives.
期刊介绍：
The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics.
Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition.
The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.
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