{"title":"具有定向弱转移的预轴的上同性","authors":"J. Ross","doi":"10.1090/JAG/684","DOIUrl":null,"url":null,"abstract":"Over a field of characteristic zero, we establish the homotopy invariance of the Nisnevich cohomology of homotopy invariant presheaves with oriented weak transfers, and the agreement of Zariski and Nisnevich cohomology for such presheaves. This generalizes a foundational result in Voevodsky's theory of motives. The main idea is to find explicit smooth representatives of the correspondences which provide the input for Voevodsky's cohomological architecture.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":"10 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Cohomology of presheaves with oriented weak transfers\",\"authors\":\"J. Ross\",\"doi\":\"10.1090/JAG/684\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Over a field of characteristic zero, we establish the homotopy invariance of the Nisnevich cohomology of homotopy invariant presheaves with oriented weak transfers, and the agreement of Zariski and Nisnevich cohomology for such presheaves. This generalizes a foundational result in Voevodsky's theory of motives. The main idea is to find explicit smooth representatives of the correspondences which provide the input for Voevodsky's cohomological architecture.\",\"PeriodicalId\":309711,\"journal\":{\"name\":\"arXiv: K-Theory and Homology\",\"volume\":\"10 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: K-Theory and Homology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/JAG/684\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: K-Theory and Homology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/JAG/684","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Cohomology of presheaves with oriented weak transfers
Over a field of characteristic zero, we establish the homotopy invariance of the Nisnevich cohomology of homotopy invariant presheaves with oriented weak transfers, and the agreement of Zariski and Nisnevich cohomology for such presheaves. This generalizes a foundational result in Voevodsky's theory of motives. The main idea is to find explicit smooth representatives of the correspondences which provide the input for Voevodsky's cohomological architecture.
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