{"title":"Hoffmann-Totaro猜想的终极证明","authors":"N. Karpenko","doi":"10.4171/jems/1211","DOIUrl":null,"url":null,"abstract":"We prove the last open case of the conjecture on the possible values of the first isotropy index of an anisotropic quadratic form over a field. It was initially stated by Detlev Hoffmann for fields of characteristic ̸= 2 and then extended to arbitrary characteristic by Burt Totaro. The initial statement was proven by the author in 2002. In characteristic 2, the case of a totally singular quadratic form was done by Stephen Scully in 2015 and the nonsingular case by Eric Primozic in early 2019.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2022-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"An ultimate proof of Hoffmann–Totaro’s conjecture\",\"authors\":\"N. Karpenko\",\"doi\":\"10.4171/jems/1211\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove the last open case of the conjecture on the possible values of the first isotropy index of an anisotropic quadratic form over a field. It was initially stated by Detlev Hoffmann for fields of characteristic ̸= 2 and then extended to arbitrary characteristic by Burt Totaro. The initial statement was proven by the author in 2002. In characteristic 2, the case of a totally singular quadratic form was done by Stephen Scully in 2015 and the nonsingular case by Eric Primozic in early 2019.\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2022-01-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/jems/1211\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/jems/1211","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
We prove the last open case of the conjecture on the possible values of the first isotropy index of an anisotropic quadratic form over a field. It was initially stated by Detlev Hoffmann for fields of characteristic ̸= 2 and then extended to arbitrary characteristic by Burt Totaro. The initial statement was proven by the author in 2002. In characteristic 2, the case of a totally singular quadratic form was done by Stephen Scully in 2015 and the nonsingular case by Eric Primozic in early 2019.
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