{"title":"通过Picard方案的abelian方案下的托子","authors":"R. Lodh","doi":"10.4171/rsmup/91","DOIUrl":null,"url":null,"abstract":"Given a torsor P under a principally polarised abelian scheme J , projective over a noetherian base, we use the Picard scheme of P to write down an explicit extension of Z by J giving the class of P . As an application we give a version of Bhatt’s period-index result valid over an arbitrary noetherian base.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"52 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Torsors under abelian schemes via Picard schemes\",\"authors\":\"R. Lodh\",\"doi\":\"10.4171/rsmup/91\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given a torsor P under a principally polarised abelian scheme J , projective over a noetherian base, we use the Picard scheme of P to write down an explicit extension of Z by J giving the class of P . As an application we give a version of Bhatt’s period-index result valid over an arbitrary noetherian base.\",\"PeriodicalId\":20997,\"journal\":{\"name\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"volume\":\"52 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-07-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/rsmup/91\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rendiconti del Seminario Matematico della Università di Padova","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/rsmup/91","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Given a torsor P under a principally polarised abelian scheme J , projective over a noetherian base, we use the Picard scheme of P to write down an explicit extension of Z by J giving the class of P . As an application we give a version of Bhatt’s period-index result valid over an arbitrary noetherian base.
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