{"title":"Troisième groupe de cohomologie non\nramifiée des hypersurfaces de Fano","authors":"Jean-Louis Colliot-Th'elene","doi":"10.2140/TUNIS.2019.1.47","DOIUrl":null,"url":null,"abstract":"We establish the vanishing of the third unramified cohomology group for many types of Fano hypersurfaces in projective space over an algebraically closed field of arbitrary characteristic, and over a finite field. For cubic hypersurfaces over a finite field, the case of fourfolds remains open. \n--- \nSur un corps alg\\'ebriquement clos et sur un corps fini, on \\'etablit de nouveaux r\\'esultats d'annulation pour la cohomologie non ramifi\\'ee de degr\\'e 3 pour de nombreux types d'hypersurfaces de Fano. Le cas des hypersurfaces cubiques de dimension 4 sur un corps fini reste ouvert.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2017-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/TUNIS.2019.1.47","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tunisian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/TUNIS.2019.1.47","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 5
Abstract
We establish the vanishing of the third unramified cohomology group for many types of Fano hypersurfaces in projective space over an algebraically closed field of arbitrary characteristic, and over a finite field. For cubic hypersurfaces over a finite field, the case of fourfolds remains open.
---
Sur un corps alg\'ebriquement clos et sur un corps fini, on \'etablit de nouveaux r\'esultats d'annulation pour la cohomologie non ramifi\'ee de degr\'e 3 pour de nombreux types d'hypersurfaces de Fano. Le cas des hypersurfaces cubiques de dimension 4 sur un corps fini reste ouvert.
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