{"title":"范诺超曲面的第三个非分支上同调群","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":"{\"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}","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}
Troisième groupe de cohomologie non
ramifiée des hypersurfaces de Fano
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.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
