{"title":"FINITENESS OF OVER TOTALLY REAL FIELDS","authors":"V. Kolyvagin, D. Y. Logachëv","doi":"10.1070/IM1992V039N01ABEH002228","DOIUrl":null,"url":null,"abstract":"Kolyvagin's method for the proof of the finiteness of is extended to abelian varieties with real multiplication, of -rank 0, defined over totally real fields, if they are factors of the Jacobians of Shimura curves. The finiteness of for such a variety is proved, starting from the conditions that a Heegner point on it is not a torsion point.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"25","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-izvestiya","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/IM1992V039N01ABEH002228","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 25
Abstract
Kolyvagin's method for the proof of the finiteness of is extended to abelian varieties with real multiplication, of -rank 0, defined over totally real fields, if they are factors of the Jacobians of Shimura curves. The finiteness of for such a variety is proved, starting from the conditions that a Heegner point on it is not a torsion point.
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