{"title":"Some remarks on the smash-nilpotence conjecture","authors":"Bruno Kahn","doi":"10.1016/j.indag.2024.05.009","DOIUrl":"https://doi.org/10.1016/j.indag.2024.05.009","url":null,"abstract":"We discuss cases where Voevodsky’s smash nilpotence conjecture is known, and give a few new ones. In particular we explain a theorem of the cube for 1-cycles, which is due to Oussama Ouriachi.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141553293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Chow–Lefschetz motives","authors":"Bruno Kahn","doi":"10.1016/j.indag.2024.04.007","DOIUrl":"https://doi.org/10.1016/j.indag.2024.04.007","url":null,"abstract":"We develop Milne’s theory of Lefschetz motives for general adequate equivalence relations and over a not necessarily algebraically closed base field. The corresponding categories turn out to enjoy all properties predicted by standard and less standard conjectures, in a stronger way: algebraic and numerical equivalences agree in this context. We also compute the Tannakian group associated to a Weil cohomology in a different and more conceptual way than Milne’s case-by-case approach.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"131 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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